diff --git a/tools/pybind11Tools.cmake b/tools/pybind11Tools.cmake
index 323135399..cc5ca21ca 100644
--- a/tools/pybind11Tools.cmake
+++ b/tools/pybind11Tools.cmake
@@ -45,31 +45,25 @@ list(APPEND CMAKE_MODULE_PATH "${CMAKE_CURRENT_LIST_DIR}")
 find_package(PythonLibsNew ${PYBIND11_PYTHON_VERSION} MODULE REQUIRED ${_pybind11_quiet})
 list(REMOVE_AT CMAKE_MODULE_PATH -1)
 
+# Makes a normal variable a cached variable
+macro(_PYBIND11_PROMOTE_TO_CACHE NAME)
+  set(_tmp_ptc "${${NAME}}")
+  # CMake 3.21 complains if a cached variable is shadowed by a normal one
+  unset(${NAME})
+  set(${NAME}
+      "${_tmp_ptc}"
+      CACHE INTERNAL "")
+endmacro()
+
 # Cache variables so pybind11_add_module can be used in parent projects
-set(PYTHON_INCLUDE_DIRS
-    ${PYTHON_INCLUDE_DIRS}
-    CACHE INTERNAL "")
-set(PYTHON_LIBRARIES
-    ${PYTHON_LIBRARIES}
-    CACHE INTERNAL "")
-set(PYTHON_MODULE_PREFIX
-    ${PYTHON_MODULE_PREFIX}
-    CACHE INTERNAL "")
-set(PYTHON_MODULE_EXTENSION
-    ${PYTHON_MODULE_EXTENSION}
-    CACHE INTERNAL "")
-set(PYTHON_VERSION_MAJOR
-    ${PYTHON_VERSION_MAJOR}
-    CACHE INTERNAL "")
-set(PYTHON_VERSION_MINOR
-    ${PYTHON_VERSION_MINOR}
-    CACHE INTERNAL "")
-set(PYTHON_VERSION
-    ${PYTHON_VERSION}
-    CACHE INTERNAL "")
-set(PYTHON_IS_DEBUG
-    "${PYTHON_IS_DEBUG}"
-    CACHE INTERNAL "")
+_pybind11_promote_to_cache(PYTHON_INCLUDE_DIRS)
+_pybind11_promote_to_cache(PYTHON_LIBRARIES)
+_pybind11_promote_to_cache(PYTHON_MODULE_PREFIX)
+_pybind11_promote_to_cache(PYTHON_MODULE_EXTENSION)
+_pybind11_promote_to_cache(PYTHON_VERSION_MAJOR)
+_pybind11_promote_to_cache(PYTHON_VERSION_MINOR)
+_pybind11_promote_to_cache(PYTHON_VERSION)
+_pybind11_promote_to_cache(PYTHON_IS_DEBUG)
 
 if(PYBIND11_MASTER_PROJECT)
   if(PYTHON_MODULE_EXTENSION MATCHES "pypy")