diff --git a/run_project_tests.py b/run_project_tests.py
index 3e1a4d155..7cbce64d5 100755
--- a/run_project_tests.py
+++ b/run_project_tests.py
@@ -1061,6 +1061,10 @@ def detect_tests_to_run(only: T.Dict[str, T.List[str]], use_tmp: bool) -> T.List
                        shutil.which('nagfor') or
                        shutil.which('ifort'))
 
+    skip_cmake = ((os.environ.get('compiler') == 'msvc2015' and under_ci) or
+                  'cmake' not in tool_vers_map or
+                  not mesonlib.version_compare(tool_vers_map['cmake'], '>=3.14'))
+
     class TestCategory:
         def __init__(self, category: str, subdir: str, skip: bool = False, stdout_mandatory: bool = False):
             self.category = category                  # category name
@@ -1069,7 +1073,7 @@ def detect_tests_to_run(only: T.Dict[str, T.List[str]], use_tmp: bool) -> T.List
             self.stdout_mandatory = stdout_mandatory  # expected stdout is mandatory for tests in this category
 
     all_tests = [
-        TestCategory('cmake', 'cmake', not shutil.which('cmake') or (os.environ.get('compiler') == 'msvc2015' and under_ci) or (os.environ.get('MESON_CI_JOBNAME') == 'linux-bionic-gcc')),
+        TestCategory('cmake', 'cmake', skip_cmake),
         TestCategory('common', 'common'),
         TestCategory('native', 'native'),
         TestCategory('warning-meson', 'warning', stdout_mandatory=True),
diff --git a/test cases/cmake/11 cmake_module_path/test.json b/test cases/cmake/11 cmake_module_path/test.json
deleted file mode 100644
index 79a2b60d3..000000000
--- a/test cases/cmake/11 cmake_module_path/test.json	
+++ /dev/null
@@ -1,5 +0,0 @@
-{
-  "tools": {
-    "cmake": ">=3.12"
-  }
-}
diff --git a/test cases/cmake/19 advanced options/test.json b/test cases/cmake/19 advanced options/test.json
index 71ea812c7..29888eae2 100644
--- a/test cases/cmake/19 advanced options/test.json	
+++ b/test cases/cmake/19 advanced options/test.json	
@@ -1,8 +1,5 @@
 {
   "installed": [
     {"type": "exe", "file": "usr/bin/testEXE"}
-  ],
-  "tools": {
-    "cmake": ">=3.11"
-  }
+  ]
 }
diff --git a/test cases/cmake/2 advanced/test.json b/test cases/cmake/2 advanced/test.json
index 71ea812c7..29888eae2 100644
--- a/test cases/cmake/2 advanced/test.json	
+++ b/test cases/cmake/2 advanced/test.json	
@@ -1,8 +1,5 @@
 {
   "installed": [
     {"type": "exe", "file": "usr/bin/testEXE"}
-  ],
-  "tools": {
-    "cmake": ">=3.11"
-  }
+  ]
 }
diff --git a/test cases/cmake/3 advanced no dep/test.json b/test cases/cmake/3 advanced no dep/test.json
index c27ed82e4..e75e54a7e 100644
--- a/test cases/cmake/3 advanced no dep/test.json	
+++ b/test cases/cmake/3 advanced no dep/test.json	
@@ -4,8 +4,5 @@
     {"type": "exe", "file": "usr/bin/cm_meson_testEXE"},
     {"type": "pdb", "file": "usr/bin/cm_benchmark"},
     {"type": "exe", "file": "usr/bin/cm_benchmark"}
-  ],
-  "tools": {
-    "cmake": ">=3.11"
-  }
+  ]
 }
diff --git a/test cases/unit/84 nested subproject regenerate depends/meson.build b/test cases/unit/84 nested subproject regenerate depends/meson.build
index 569888164..a8d213887 100644
--- a/test cases/unit/84 nested subproject regenerate depends/meson.build	
+++ b/test cases/unit/84 nested subproject regenerate depends/meson.build	
@@ -1,5 +1,9 @@
 project('nested subproject regenerate depends', 'c')
 
+if not find_program('cmake', required: false, version: '>=3.14').found()
+  error('MESON_SKIP_TEST cmake >= 3.14 not available.')
+endif
+
 s = subproject('sub1')
 
 # This is needed to make msbuild noop check work correctly
diff --git a/unittests/allplatformstests.py b/unittests/allplatformstests.py
index 8425cf539..f0e27e91a 100644
--- a/unittests/allplatformstests.py
+++ b/unittests/allplatformstests.py
@@ -3740,8 +3740,6 @@ class AllPlatformTests(BasePlatformTests):
         # This checks a bug where if a non-meson project is used as a third
         # level (or deeper) subproject it doesn't cause a rebuild if the build
         # files for that project are changed
-        if os.environ.get('MESON_CI_JOBNAME') == 'linux-bionic-gcc':
-            raise SkipTest('Unsupported CMake version')
         testdir = os.path.join(self.unit_test_dir, '84 nested subproject regenerate depends')
         cmakefile = Path(testdir) / 'subprojects' / 'sub2' / 'CMakeLists.txt'
         self.init(testdir)