diff --git a/.github/workflows/ci-test-package-cmake.yml b/.github/workflows/ci-test-package-cmake.yml
index d58db7083..5367355de 100644
--- a/.github/workflows/ci-test-package-cmake.yml
+++ b/.github/workflows/ci-test-package-cmake.yml
@@ -203,7 +203,13 @@ jobs:
         run: |
           cmake --preset conan-default -Dmp-units_DIR=../build -Bbuild/local
           cmake --build build/local --config ${{ matrix.build_type }}
+      - name: Run test_package-headers (local build)
+        shell: bash
+        working-directory: test_package/build/local/${{ matrix.build_type }}
+        run: |
+          ./test_package-headers
       - name: Run test_package (local build)
+        if: matrix.config.cxx_modules == 'True'
         shell: bash
         working-directory: test_package/build/local/${{ matrix.build_type }}
         run: |
@@ -223,7 +229,13 @@ jobs:
         run: |
           cmake --preset conan-default -DCMAKE_INSTALL_PREFIX=../out -Bbuild/install
           cmake --build build/install --config ${{ matrix.build_type }}
+      - name: Run test_package-headers (installation)
+        shell: bash
+        working-directory: test_package/build/install/${{ matrix.build_type }}
+        run: |
+          ./test_package-headers
       - name: Run test_package (installation)
+        if: matrix.config.cxx_modules == 'True'
         shell: bash
         working-directory: test_package/build/install/${{ matrix.build_type }}
         run: |
diff --git a/conanfile.py b/conanfile.py
index 7b9c1853b..8026ddf63 100644
--- a/conanfile.py
+++ b/conanfile.py
@@ -216,7 +216,7 @@ def requirements(self):
                 self.requires("fmt/11.0.1", transitive_headers=True)
 
     def build_requirements(self):
-        self.tool_requires("cmake/[>=3.30 <4]")
+        self.tool_requires("cmake/[>=3.31 <4]")
         if self._build_all:
             if not self.options.freestanding:
                 self.test_requires("catch2/3.7.0")
diff --git a/test_package/CMakeLists.txt b/test_package/CMakeLists.txt
index e57d1d8b3..fa7cc1a85 100644
--- a/test_package/CMakeLists.txt
+++ b/test_package/CMakeLists.txt
@@ -20,10 +20,20 @@
 # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 # SOFTWARE.
 
-cmake_minimum_required(VERSION 3.25)
+cmake_minimum_required(VERSION 3.30.5)
 project(test_package LANGUAGES CXX)
 
+message(STATUS "MP_UNITS_BUILD_CXX_MODULES: ${MP_UNITS_BUILD_CXX_MODULES}")
+message(STATUS "MP_UNITS_API_STD_FORMAT: ${MP_UNITS_API_STD_FORMAT}")
+
 find_package(mp-units REQUIRED)
 
-add_executable(test_package test_package.cpp)
-target_link_libraries(test_package PRIVATE mp-units::mp-units)
+add_executable(test_package-headers test_package.cpp)
+target_compile_features(test_package-headers PRIVATE cxx_std_20)
+target_link_libraries(test_package-headers PRIVATE mp-units::mp-units)
+
+if(MP_UNITS_BUILD_CXX_MODULES)
+    add_executable(test_package test_package.cpp)
+    target_compile_features(test_package PRIVATE cxx_std_20)
+    target_link_libraries(test_package PRIVATE mp-units::mp-units)
+endif()
diff --git a/test_package/conanfile.py b/test_package/conanfile.py
index f81cf891b..882f57199 100644
--- a/test_package/conanfile.py
+++ b/test_package/conanfile.py
@@ -42,6 +42,7 @@ def generate(self):
         opt = self.dependencies["mp-units"].options
         if opt.cxx_modules:
             tc.cache_variables["CMAKE_CXX_SCAN_FOR_MODULES"] = True
+            tc.cache_variables["MP_UNITS_BUILD_CXX_MODULES"] = True
         if opt.import_std:
             tc.cache_variables["CMAKE_CXX_MODULE_STD"] = True
             # Current experimental support according to `Help/dev/experimental.rst`
@@ -64,5 +65,8 @@ def build(self):
 
     def test(self):
         if can_run(self):
-            bin_path = os.path.join(self.cpp.build.bindirs[0], "test_package")
+            if self.dependencies["mp-units"].options.cxx_modules:
+                bin_path = os.path.join(self.cpp.build.bindirs[0], "test_package")
+                self.run(bin_path, env="conanrun")
+            bin_path = os.path.join(self.cpp.build.bindirs[0], "test_package-headers")
             self.run(bin_path, env="conanrun")