diff --git a/core/reorder/nested_dissection.cpp b/core/reorder/nested_dissection.cpp
index 2703f47d3b7..ff7bb06dc93 100644
--- a/core/reorder/nested_dissection.cpp
+++ b/core/reorder/nested_dissection.cpp
@@ -69,7 +69,7 @@ std::string metis_error_message(idx_t metis_error)
     case METIS_OK:
         return "METIS_OK";
     default:
-        return "<unknown>";
+        return "<" + std::to_string(metis_error) + ">";
     }
 }
 
@@ -87,7 +87,12 @@ std::array<idx_t, METIS_NOPTIONS> build_metis_options(
         result[pair.first] = pair.second;
     }
     // make sure users don't accidentally switch on 1-based indexing
-    result[METIS_OPTION_NUMBERING] = 0;
+    if (options.find(METIS_OPTION_NUMBERING) != options.end() &&
+        options.at(METIS_OPTION_NUMBERING) != 0) {
+        throw MetisError(
+            __FILE__, __LINE__, "build_metis_options",
+            "METIS_OPTION_NUMBERING: Only 0-based indexing is supported");
+    }
     return result;
 }
 
@@ -151,7 +156,7 @@ NestedDissection<ValueType, IndexType>::NestedDissection(
 template <typename ValueType, typename IndexType>
 std::unique_ptr<matrix::Permutation<IndexType>>
 NestedDissection<ValueType, IndexType>::generate(
-    std::shared_ptr<const matrix_type> system_matrix) const
+    std::shared_ptr<const LinOp> system_matrix) const
 {
     auto product =
         std::unique_ptr<permutation_type>(static_cast<permutation_type*>(
diff --git a/core/test/reorder/CMakeLists.txt b/core/test/reorder/CMakeLists.txt
index d654c5d78fc..383eb171b8b 100644
--- a/core/test/reorder/CMakeLists.txt
+++ b/core/test/reorder/CMakeLists.txt
@@ -1,2 +1,5 @@
+if(GINKGO_HAVE_METIS)
+    ginkgo_create_test(nested_dissection)
+endif()
 ginkgo_create_test(rcm)
 ginkgo_create_test(scaled_reordered)
diff --git a/core/test/reorder/nested_dissection.cpp b/core/test/reorder/nested_dissection.cpp
new file mode 100644
index 00000000000..e738883d977
--- /dev/null
+++ b/core/test/reorder/nested_dissection.cpp
@@ -0,0 +1,71 @@
+/*******************************<GINKGO LICENSE>******************************
+Copyright (c) 2017-2023, the Ginkgo authors
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in the
+documentation and/or other materials provided with the distribution.
+
+3. Neither the name of the copyright holder nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+******************************<GINKGO LICENSE>*******************************/
+
+#include <ginkgo/core/reorder/nested_dissection.hpp>
+
+
+#include <memory>
+
+
+#include <gtest/gtest.h>
+
+
+#include <ginkgo/core/base/executor.hpp>
+
+
+#include "core/test/utils.hpp"
+
+
+namespace {
+
+class NestedDissection : public ::testing::Test {
+protected:
+    using value_type = double;
+    using index_type = int;
+    using reorder_type =
+        gko::experimental::reorder::NestedDissection<value_type, index_type>;
+
+    NestedDissection()
+        : exec(gko::ReferenceExecutor::create()),
+          nd_factory(reorder_type::build().on(exec))
+    {}
+
+    std::shared_ptr<const gko::Executor> exec;
+    std::unique_ptr<reorder_type> nd_factory;
+};
+
+TEST_F(NestedDissection, KnowsItsExecutor)
+{
+    ASSERT_EQ(this->nd_factory->get_executor(), this->exec);
+}
+
+}  // namespace
diff --git a/include/ginkgo/core/reorder/nested_dissection.hpp b/include/ginkgo/core/reorder/nested_dissection.hpp
index d5e7967eb69..738dd6d8a0e 100644
--- a/include/ginkgo/core/reorder/nested_dissection.hpp
+++ b/include/ginkgo/core/reorder/nested_dissection.hpp
@@ -112,6 +112,11 @@ class NestedDissection
         }
     };
 
+    /**
+     * Returns the parameters used to construct the factory.
+     */
+    const parameters_type& get_parameters() { return parameters_; }
+
     /**
      * @copydoc LinOpFactory::generate
      * @note This function overrides the default LinOpFactory::generate to
@@ -120,7 +125,7 @@ class NestedDissection
      *       It is only necessary because smart pointers aren't covariant.
      */
     std::unique_ptr<permutation_type> generate(
-        std::shared_ptr<const matrix_type> system_matrix) const;
+        std::shared_ptr<const LinOp> system_matrix) const;
 
     /** Creates a new parameter_type to set up the factory. */
     static parameters_type build() { return {}; }
diff --git a/reference/test/reorder/CMakeLists.txt b/reference/test/reorder/CMakeLists.txt
index 77017df1604..766decfb749 100644
--- a/reference/test/reorder/CMakeLists.txt
+++ b/reference/test/reorder/CMakeLists.txt
@@ -1,3 +1,6 @@
+if(GINKGO_HAVE_METIS)
+    ginkgo_create_test(nested_dissection)
+endif()
 ginkgo_create_test(rcm)
 ginkgo_create_test(rcm_kernels)
 ginkgo_create_test(scaled_reordered)
diff --git a/reference/test/reorder/nested_dissection.cpp b/reference/test/reorder/nested_dissection.cpp
new file mode 100644
index 00000000000..ab1cd073f5a
--- /dev/null
+++ b/reference/test/reorder/nested_dissection.cpp
@@ -0,0 +1,135 @@
+/*******************************<GINKGO LICENSE>******************************
+Copyright (c) 2017-2023, the Ginkgo authors
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in the
+documentation and/or other materials provided with the distribution.
+
+3. Neither the name of the copyright holder nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+******************************<GINKGO LICENSE>*******************************/
+
+#include <ginkgo/core/reorder/nested_dissection.hpp>
+
+
+#include <memory>
+
+
+#include <gtest/gtest.h>
+#include GKO_METIS_HEADER
+
+
+#include <ginkgo/core/base/executor.hpp>
+#include <ginkgo/core/matrix/csr.hpp>
+#include <ginkgo/core/matrix/dense.hpp>
+#include <ginkgo/core/matrix/sparsity_csr.hpp>
+
+
+#include "core/test/utils.hpp"
+#include "core/test/utils/assertions.hpp"
+#include "ginkgo/core/base/exception.hpp"
+
+
+namespace {
+
+
+template <typename IndexType>
+class NestedDissection : public ::testing::Test {
+protected:
+    using value_type = double;
+    using index_type = IndexType;
+    using reorder_type =
+        gko::experimental::reorder::NestedDissection<value_type, index_type>;
+    using Mtx = gko::matrix::Dense<value_type>;
+    NestedDissection()
+        : exec(gko::ReferenceExecutor::create()),
+          nd_factory(reorder_type::build().on(exec)),
+          star_mtx{gko::initialize<Mtx>({{1.0, 1.0, 1.0, 1.0},
+                                         {1.0, 1.0, 0.0, 0.0},
+                                         {1.0, 0.0, 1.0, 0.0},
+                                         {1.0, 0.0, 0.0, 1.0}},
+                                        exec)}
+    {}
+
+    std::shared_ptr<const gko::Executor> exec;
+    std::shared_ptr<Mtx> star_mtx;
+    std::unique_ptr<reorder_type> nd_factory;
+};
+
+TYPED_TEST_SUITE(NestedDissection, gko::test::IndexTypes,
+                 TypenameNameGenerator);
+
+
+TYPED_TEST(NestedDissection, HasSensibleDefaults)
+{
+    using reorder_type = typename TestFixture::reorder_type;
+
+    auto factory = reorder_type::build().on(this->exec);
+
+    ASSERT_TRUE(factory->get_parameters().options.empty());
+}
+
+
+TYPED_TEST(NestedDissection, FailsWithInvalidOption)
+{
+    using value_type = typename TestFixture::value_type;
+    using reorder_type = typename TestFixture::reorder_type;
+    auto factory = reorder_type::build()
+                       .with_options({{METIS_NOPTIONS, 0}})
+                       .on(this->exec);
+
+    ASSERT_THROW(factory->generate(this->star_mtx), gko::MetisError);
+}
+
+
+TYPED_TEST(NestedDissection, FailsWithOneBasedIndexing)
+{
+    using value_type = typename TestFixture::value_type;
+    using reorder_type = typename TestFixture::reorder_type;
+    auto factory = reorder_type::build()
+                       .with_options({{METIS_OPTION_NUMBERING, 1}})
+                       .on(this->exec);
+
+    ASSERT_THROW(factory->generate(this->star_mtx), gko::MetisError);
+}
+
+
+TYPED_TEST(NestedDissection, ComputesSensiblePermutation)
+{
+    auto perm = this->nd_factory->generate(this->star_mtx);
+
+    auto perm_array = gko::make_array_view(this->exec, perm->get_size()[0],
+                                           perm->get_permutation());
+    auto permuted = gko::as<typename TestFixture::Mtx>(
+        this->star_mtx->permute(&perm_array));
+    GKO_ASSERT_MTX_NEAR(permuted,
+                        I<I<double>>({{1.0, 0.0, 0.0, 1.0},
+                                      {0.0, 1.0, 0.0, 1.0},
+                                      {0.0, 0.0, 1.0, 1.0},
+                                      {1.0, 1.0, 1.0, 1.0}}),
+                        0.0);
+}
+
+
+}  // namespace