Index: clang-tools-extra/clang-tidy/cppcoreguidelines/VirtualClassDestructorCheck.cpp
===================================================================
--- clang-tools-extra/clang-tidy/cppcoreguidelines/VirtualClassDestructorCheck.cpp
+++ clang-tools-extra/clang-tidy/cppcoreguidelines/VirtualClassDestructorCheck.cpp
@@ -23,10 +23,14 @@
   ast_matchers::internal::Matcher<CXXRecordDecl> InheritsVirtualMethod =
       hasAnyBase(hasType(cxxRecordDecl(has(cxxMethodDecl(isVirtual())))));
 
+  ast_matchers::internal::Matcher<CXXRecordDecl> InheritsVirtualDestructor =
+      hasAnyBase(hasType(cxxRecordDecl(has(cxxDestructorDecl(isVirtual())))));
+
   Finder->addMatcher(
       cxxRecordDecl(
           anyOf(has(cxxMethodDecl(isVirtual())), InheritsVirtualMethod),
           unless(anyOf(
+              InheritsVirtualDestructor,
               has(cxxDestructorDecl(isPublic(), isVirtual())),
               has(cxxDestructorDecl(isProtected(), unless(isVirtual()))))))
           .bind("ProblematicClassOrStruct"),
Index: clang-tools-extra/test/clang-tidy/checkers/cppcoreguidelines-virtual-class-destructor.cpp
===================================================================
--- clang-tools-extra/test/clang-tidy/checkers/cppcoreguidelines-virtual-class-destructor.cpp
+++ clang-tools-extra/test/clang-tidy/checkers/cppcoreguidelines-virtual-class-destructor.cpp
@@ -202,3 +202,22 @@
   void m();
 };
 // inherits virtual method
+
+// The following two checks cover bug https://bugs.llvm.org/show_bug.cgi?id=51912
+// Forward declarations
+// CHECK-MESSAGES-NOT: :[[@LINE+1]]:8: warning: destructor of 'ForwardDeclaredStruct' is public and non-virtual [cppcoreguidelines-virtual-class-destructor]
+struct ForwardDeclaredStruct;
+
+struct ForwardDeclaredStruct : PublicVirtualBaseStruct {
+};
+
+// Templates
+// CHECK-MESSAGES-NOT: :[[@LINE+2]]:8: warning: destructor of 'TemplatedDerived' is public and non-virtual [cppcoreguidelines-virtual-class-destructor]
+template <typename T>
+struct TemplatedDerived : PublicVirtualBaseStruct {
+};
+
+// Templates need to be instantiated for diagnostics to show up
+void test_templates() {
+  TemplatedDerived<int> x;
+}