diff --git a/core/tests/Drupal/Tests/Constraints/ResponseHeaderExists.php b/core/tests/Drupal/Tests/Constraints/ResponseHeaderExists.php
new file mode 100644
index 0000000000..3d14f5644f
--- /dev/null
+++ b/core/tests/Drupal/Tests/Constraints/ResponseHeaderExists.php
@@ -0,0 +1,53 @@
+<?php
+
+namespace Drupal\Tests\Constraints;
+
+use PHPUnit\Framework\Constraint\Constraint;
+
+/**
+ * Asserts that a response header exists.
+ */
+class ResponseHeaderExists extends Constraint {
+
+  /**
+   * The header to be tested.
+   *
+   * @var string
+   */
+  protected $header;
+
+  /**
+   * Constructs a ResponseHeaderExists object.
+   *
+   * @param string $header
+   *   The header to be tested.
+   */
+  public function __construct($header) {
+    $this->header = $header;
+  }
+
+  /**
+   * {@inheritdoc}
+   */
+  protected function matches($other): bool {
+    if (is_array($other)) {
+      return array_key_exists($this->header, $other);
+    }
+
+    return FALSE;
+  }
+
+  /**
+   * {@inheritdoc}
+   */
+  public function toString(): string {
+    return 'has a ' . $this->exporter()->export($this->header) . ' header';
+  }
+
+  /**
+   * {@inheritdoc}
+   */
+  protected function failureDescription($other): string {
+    return 'the response ' . $this->toString();
+  }
+}
diff --git a/core/tests/Drupal/Tests/WebAssert.php b/core/tests/Drupal/Tests/WebAssert.php
index a3bf6b0704..3e67197681 100644
--- a/core/tests/Drupal/Tests/WebAssert.php
+++ b/core/tests/Drupal/Tests/WebAssert.php
@@ -10,6 +10,7 @@
 use Behat\Mink\Session;
 use Drupal\Component\Utility\Html;
 use Drupal\Core\Url;
+use Drupal\Tests\Constraints\ResponseHeaderExists;
 use PHPUnit\Framework\Assert;
 use PHPUnit\Framework\Constraint\ArrayHasKey;
 use PHPUnit\Framework\Constraint\LogicalNot;
@@ -65,11 +66,8 @@ protected function cleanUrl($url) {
    *   The name of the header entry to check existence of.
    */
   public function responseHeaderExists(string $name, string $message = ''): void {
-    if ($message === '') {
-      $message = "Failed asserting that the response has a '$name' header.";
-    }
     $headers = $this->session->getResponseHeaders();
-    $constraint = new ArrayHasKey($name);
+    $constraint = new ResponseHeaderExists($name);
     Assert::assertThat($headers, $constraint, $message);
   }
 
@@ -80,12 +78,9 @@ public function responseHeaderExists(string $name, string $message = ''): void {
    *   The name of the header entry to check existence of.
    */
   public function responseHeaderDoesNotExist(string $name, string $message = ''): void {
-    if ($message === '') {
-      $message = "Failed asserting that the response does not have a '$name' header.";
-    }
     $headers = $this->session->getResponseHeaders();
     $constraint = new LogicalNot(
-      new ArrayHasKey($name)
+      new ResponseHeaderExists($name)
     );
     Assert::assertThat($headers, $constraint, $message);
   }