diff --git a/lib/rubocop/cop/internal_affairs/cop_description.rb b/lib/rubocop/cop/internal_affairs/cop_description.rb
index 769be81acfde..d5097d4d3bc9 100644
--- a/lib/rubocop/cop/internal_affairs/cop_description.rb
+++ b/lib/rubocop/cop/internal_affairs/cop_description.rb
@@ -114,7 +114,7 @@ def comment_index(node, comment_line)
         end
 
         def relevant_file?(file)
-          file.match?(%r{/cop/.*\.rb\z})
+          file.match?(%r{/cop/.*\.rb\z}) && super
         end
       end
     end
diff --git a/lib/rubocop/cop/internal_affairs/useless_message_assertion.rb b/lib/rubocop/cop/internal_affairs/useless_message_assertion.rb
index c31a4b571a6a..bb0193b40d59 100644
--- a/lib/rubocop/cop/internal_affairs/useless_message_assertion.rb
+++ b/lib/rubocop/cop/internal_affairs/useless_message_assertion.rb
@@ -46,7 +46,7 @@ def assertions_using_described_class_msg
 
         # Only process spec files
         def relevant_file?(file)
-          file.end_with?('_spec.rb')
+          file.end_with?('_spec.rb') && super
         end
       end
     end
diff --git a/spec/rubocop/cop/internal_affairs/cop_description_spec.rb b/spec/rubocop/cop/internal_affairs/cop_description_spec.rb
index 65b973a4d688..26136ec57142 100644
--- a/spec/rubocop/cop/internal_affairs/cop_description_spec.rb
+++ b/spec/rubocop/cop/internal_affairs/cop_description_spec.rb
@@ -152,4 +152,33 @@ class Foo < Base
       RUBY
     end
   end
+
+  context 'when the file is excluded' do
+    before do
+      allow_any_instance_of(described_class).to receive(:relevant_file?).and_call_original # rubocop:disable RSpec/AnyInstance
+    end
+
+    let(:config) do
+      RuboCop::Config.new(
+        'InternalAffairs/CopDescription' => { 'Exclude' => ['**/example_cop.rb'] }
+      )
+    end
+
+    it 'does not register an offense' do
+      expect_no_offenses(<<~RUBY, 'lib/rubocop/cop/example_cop.rb')
+        module RuboCop
+          module Cop
+            module Lint
+              #
+              # Checks some problem
+              #
+              # ...
+              class Foo < Base
+              end
+            end
+          end
+        end
+      RUBY
+    end
+  end
 end
diff --git a/spec/rubocop/cop/internal_affairs/useless_message_assertion_spec.rb b/spec/rubocop/cop/internal_affairs/useless_message_assertion_spec.rb
index 80bc2c889de3..c822d7bd1831 100644
--- a/spec/rubocop/cop/internal_affairs/useless_message_assertion_spec.rb
+++ b/spec/rubocop/cop/internal_affairs/useless_message_assertion_spec.rb
@@ -41,4 +41,18 @@
   it 'does not register an offense and no error when empty file' do
     expect_no_offenses('', 'example_spec.rb')
   end
+
+  context 'when the file is excluded' do
+    let(:config) do
+      RuboCop::Config.new(
+        'InternalAffairs/UselessMessageAssertion' => { 'Exclude' => ['**/example_spec.rb'] }
+      )
+    end
+
+    it 'does not register an offense' do
+      expect_no_offenses(<<~RUBY, 'example_spec.rb')
+        let(:msg) { described_class::MSG }
+      RUBY
+    end
+  end
 end