diff --git a/core/modules/link/tests/src/Unit/Plugin/migrate/cckfield/LinkCckTest.php b/core/modules/link/tests/src/Unit/Plugin/migrate/cckfield/LinkCckTest.php
index dc3fe7731e..b908bbe902 100644
--- a/core/modules/link/tests/src/Unit/Plugin/migrate/cckfield/LinkCckTest.php
+++ b/core/modules/link/tests/src/Unit/Plugin/migrate/cckfield/LinkCckTest.php
@@ -11,6 +11,8 @@
  * @coversDefaultClass \Drupal\link\Plugin\migrate\cckfield\LinkField
  * @group link
  * @group legacy
+ * @arunInSeparateProcess
+ * @apreserveGlobalState disabled
  */
 class LinkCckTest extends UnitTestCase {
 
@@ -46,8 +48,7 @@ protected function setUp() {
 
   /**
    * @covers ::processCckFieldValues
-   * @expectedDeprecation CckFieldPluginBase is deprecated in Drupal 8.3.x and will be be removed before Drupal 9.0.x. Use \Drupal\migrate_drupal\Plugin\migrate\field\FieldPluginBase instead.
-   * @expectedDeprecation MigrateCckFieldInterface is deprecated in Drupal 8.3.x and will be removed before Drupal 9.0.x. Use \Drupal\migrate_drupal\Annotation\MigrateField instead.
+   * @expectedDeprecation LinkField is deprecated in Drupal 8.3.x and will be be removed before Drupal 9.0.x. Use \Drupal\link\Plugin\migrate\field\d6\LinkField instead.
    */
   public function testProcessCckFieldValues() {
     $this->plugin->processCckFieldValues($this->migration, 'somefieldname', []);
diff --git a/core/tests/Drupal/Tests/Core/Listeners/DrupalStandardsListenerDeprecationTest.php b/core/tests/Drupal/Tests/Core/Listeners/DrupalStandardsListenerDeprecationTest.php
index 048dfe1079..7c60d6825e 100644
--- a/core/tests/Drupal/Tests/Core/Listeners/DrupalStandardsListenerDeprecationTest.php
+++ b/core/tests/Drupal/Tests/Core/Listeners/DrupalStandardsListenerDeprecationTest.php
@@ -21,7 +21,6 @@
  * would trigger another deprecation error.
  *
  * @group Listeners
- * @group legacy
  *
  * @coversDefaultClass \Drupal\deprecation_test\Deprecation\DrupalStandardsListenerDeprecatedClass
  */
@@ -30,8 +29,6 @@ class DrupalStandardsListenerDeprecationTest extends UnitTestCase {
   /**
    * Exercise DrupalStandardsListener's coverage validation.
    *
-   * @expectedDeprecation Drupal\deprecation_test\Deprecation\DrupalStandardsListenerDeprecatedClass is deprecated.
-   *
    * @covers ::testFunction
    */
   public function testDeprecation() {
diff --git a/core/tests/Drupal/Tests/Listeners/DrupalStandardsListenerTrait.php b/core/tests/Drupal/Tests/Listeners/DrupalStandardsListenerTrait.php
index 2676c46a4f..0ad0e1e239 100644
--- a/core/tests/Drupal/Tests/Listeners/DrupalStandardsListenerTrait.php
+++ b/core/tests/Drupal/Tests/Listeners/DrupalStandardsListenerTrait.php
@@ -143,6 +143,28 @@ private function checkValidCoversForTest(TestCase $test) {
     }
   }
 
+  /**
+   * Handles errors to ensure deprecation messages are not triggered.
+   *
+   * @param int $type
+   *   The severity level of the error.
+   * @param string $msg
+   *   The error message.
+   * @param $file
+   *   The file that caused the error.
+   * @param $line
+   *   The line number that caused the error.
+   * @param array $context
+   *   The error context.
+   */
+  public static function errorHandler($type, $msg, $file, $line, $context = array()) {
+    if ($type === E_USER_DEPRECATED) {
+      return;
+    }
+    $error_handler = class_exists('PHPUnit_Util_ErrorHandler') ? 'PHPUnit_Util_ErrorHandler' : 'PHPUnit\Util\ErrorHandler';
+    return $error_handler::handleError($type, $msg, $file, $line, $context);
+  }
+
   /**
    * Reacts to the end of a test.
    *
@@ -166,7 +188,11 @@ private function doEndTest($test, $time) {
     // our purpose, so we have to distinguish between the different known
     // subclasses.
     if ($test instanceof TestCase) {
+      // Change the error handler to ensure deprecation messages are not
+      // triggered.
+      set_error_handler([$this, 'errorHandler']);
       $this->checkValidCoversForTest($test);
+      restore_error_handler();
     }
     elseif ($this->isTestSuite($test)) {
       foreach ($test->getGroupDetails() as $tests) {