diff --git a/src/TestSuite/Constraint/Response/HeaderContains.php b/src/TestSuite/Constraint/Response/HeaderContains.php
index 7aee0cb1ed3..ce0d1939e23 100644
--- a/src/TestSuite/Constraint/Response/HeaderContains.php
+++ b/src/TestSuite/Constraint/Response/HeaderContains.php
@@ -13,12 +13,10 @@
  */
 namespace Cake\TestSuite\Constraint\Response;
 
-use PHPUnit\Framework\AssertionFailedError;
-
 /**
  * HeaderContains
  */
-class HeaderContains extends Header
+class HeaderContains extends HeaderEquals
 {
 
     /**
@@ -29,11 +27,8 @@ class HeaderContains extends Header
      */
     public function matches($other)
     {
-        if (!$this->response->hasHeader($this->headerName)) {
-            throw new AssertionFailedError(sprintf('Header `%s` was not set.', $this->headerName));
-        }
-
-        return mb_strpos($this->response->getHeaderLine($this->headerName), $other) !== false;
+        $this->value = $this->response->getHeaderLine($this->headerName);
+        return mb_strpos($this->value, $other) !== false;
     }
 
     /**
@@ -43,6 +38,6 @@ public function matches($other)
      */
     public function toString()
     {
-        return sprintf('is in header `%s`', $this->headerName);
+        return sprintf('is in header `%s`, found "%s"', $this->headerName, $this->value);
     }
 }
diff --git a/src/TestSuite/Constraint/Response/HeaderEquals.php b/src/TestSuite/Constraint/Response/HeaderEquals.php
new file mode 100644
index 00000000000..2218da264b4
--- /dev/null
+++ b/src/TestSuite/Constraint/Response/HeaderEquals.php
@@ -0,0 +1,67 @@
+<?php
+/**
+ * CakePHP(tm) : Rapid Development Framework (http://cakephp.org)
+ * Copyright (c) Cake Software Foundation, Inc. (http://cakefoundation.org)
+ *
+ * Licensed under The MIT License
+ * For full copyright and license information, please see the LICENSE.txt
+ * Redistributions of files must retain the above copyright notice
+ *
+ * @copyright     Copyright (c) Cake Software Foundation, Inc. (http://cakefoundation.org)
+ * @since         3.7.0
+ * @license       http://www.opensource.org/licenses/mit-license.php MIT License
+ */
+namespace Cake\TestSuite\Constraint\Response;
+
+use Cake\Http\Response;
+
+/**
+ * HeaderEquals
+ */
+class HeaderEquals extends ResponseBase
+{
+    /**
+     * @var string
+     */
+    protected $headerName;
+
+    /**
+     * @var string
+     */
+    protected $value;
+
+    /**
+     * Constructor.
+     *
+     * @param Response $response Response
+     * @param string $headerName Header name
+     */
+    public function __construct(Response $response, $headerName)
+    {
+        parent::__construct($response);
+
+        $this->headerName = $headerName;
+    }
+
+    /**
+     * Checks assertion
+     *
+     * @param mixed $other Expected content
+     * @return bool
+     */
+    public function matches($other)
+    {
+        $this->value = $this->response->getHeaderLine($this->headerName);
+        return $this->value === $other;
+    }
+
+    /**
+     * Assertion message
+     *
+     * @return string
+     */
+    public function toString()
+    {
+        return sprintf('equals content in header `%s`, found "%s"', $this->headerName, $this->value);
+    }
+}
diff --git a/src/TestSuite/Constraint/Response/HeaderNotSet.php b/src/TestSuite/Constraint/Response/HeaderNotSet.php
new file mode 100644
index 00000000000..a2159e394ad
--- /dev/null
+++ b/src/TestSuite/Constraint/Response/HeaderNotSet.php
@@ -0,0 +1,41 @@
+<?php
+/**
+ * CakePHP(tm) : Rapid Development Framework (http://cakephp.org)
+ * Copyright (c) Cake Software Foundation, Inc. (http://cakefoundation.org)
+ *
+ * Licensed under The MIT License
+ * For full copyright and license information, please see the LICENSE.txt
+ * Redistributions of files must retain the above copyright notice
+ *
+ * @copyright     Copyright (c) Cake Software Foundation, Inc. (http://cakefoundation.org)
+ * @since         3.7.0
+ * @license       http://www.opensource.org/licenses/mit-license.php MIT License
+ */
+namespace Cake\TestSuite\Constraint\Response;
+
+/**
+ * HeaderSet
+ */
+class HeaderNotSet extends HeaderSet
+{
+    /**
+     * Checks assertion
+     *
+     * @param mixed $other Expected content
+     * @return bool
+     */
+    public function matches($other)
+    {
+        return parent::matches($other) === false;
+    }
+
+    /**
+     * Assertion message
+     *
+     * @return string
+     */
+    public function toString()
+    {
+        return sprintf('did not have header `%s`', $this->headerName);
+    }
+}
diff --git a/src/TestSuite/Constraint/Response/Header.php b/src/TestSuite/Constraint/Response/HeaderSet.php
similarity index 71%
rename from src/TestSuite/Constraint/Response/Header.php
rename to src/TestSuite/Constraint/Response/HeaderSet.php
index a0c23d36e22..3cf80463043 100644
--- a/src/TestSuite/Constraint/Response/Header.php
+++ b/src/TestSuite/Constraint/Response/HeaderSet.php
@@ -13,12 +13,12 @@
  */
 namespace Cake\TestSuite\Constraint\Response;
 
-use PHPUnit\Framework\AssertionFailedError;
+use Cake\Http\Response;
 
 /**
- * Header
+ * HeaderSet
  */
-class Header extends ResponseBase
+class HeaderSet extends ResponseBase
 {
     /**
      * @var string
@@ -28,10 +28,10 @@ class Header extends ResponseBase
     /**
      * Constructor.
      *
-     * @param \Cake\Http\Response $response Response
+     * @param Response $response Response
      * @param string $headerName Header name
      */
-    public function __construct(\Cake\Http\Response $response, $headerName)
+    public function __construct(Response $response, $headerName)
     {
         parent::__construct($response);
 
@@ -46,11 +46,7 @@ public function __construct(\Cake\Http\Response $response, $headerName)
      */
     public function matches($other)
     {
-        if (!$this->response->hasHeader($this->headerName)) {
-            throw new AssertionFailedError(sprintf('Header `%s` was not set.', $this->headerName));
-        }
-
-        return $this->response->getHeaderLine($this->headerName) === $other;
+        return $this->response->hasHeader($this->headerName);
     }
 
     /**
diff --git a/src/TestSuite/IntegrationTestTrait.php b/src/TestSuite/IntegrationTestTrait.php
index f5477e3eeda..04207aa3edf 100644
--- a/src/TestSuite/IntegrationTestTrait.php
+++ b/src/TestSuite/IntegrationTestTrait.php
@@ -23,8 +23,10 @@
 use Cake\TestSuite\Constraint\Response\CookieNotSet;
 use Cake\TestSuite\Constraint\Response\CookieSet;
 use Cake\TestSuite\Constraint\Response\CookieEquals;
-use Cake\TestSuite\Constraint\Response\Header;
+use Cake\TestSuite\Constraint\Response\HeaderEquals;
 use Cake\TestSuite\Constraint\Response\HeaderContains;
+use Cake\TestSuite\Constraint\Response\HeaderNotSet;
+use Cake\TestSuite\Constraint\Response\HeaderSet;
 use Cake\TestSuite\Constraint\Response\StatusCode;
 use Cake\TestSuite\Constraint\Response\StatusError;
 use Cake\TestSuite\Constraint\Response\StatusFailure;
@@ -787,19 +789,11 @@ public function assertResponseCode($code, $message = null)
      */
     public function assertRedirect($url = null, $message = '')
     {
-        if (!$this->_response) {
-            $this->fail('No response set, cannot assert location header. ' . $message);
-        }
-        $result = $this->_response->getHeaderLine('Location');
-        if ($url === null) {
-            $this->assertNotEmpty($result, $message);
+        $this->assertThat(null, new HeaderSet($this->_response, 'Location'), $message);
 
-            return;
-        }
-        if (empty($result)) {
-            $this->fail('No location header set. ' . $message);
+        if ($url) {
+            $this->assertThat(Router::url($url, ['_full' => true]), new HeaderEquals($this->_response, 'Location'), $message);
         }
-        $this->assertEquals(Router::url($url, ['_full' => true]), $result, $message);
     }
 
     /**
@@ -811,14 +805,8 @@ public function assertRedirect($url = null, $message = '')
      */
     public function assertRedirectContains($url, $message = '')
     {
-        if (!$this->_response) {
-            $this->fail('No response set, cannot assert location header. ' . $message);
-        }
-        $result = $this->_response->getHeaderLine('Location');
-        if (empty($result)) {
-            $this->fail('No location header set. ' . $message);
-        }
-        $this->assertContains($url, $result, $message);
+        $this->assertThat(null, new HeaderSet($this->_response, 'Location'), $message);
+        $this->assertThat($url, new HeaderContains($this->_response, 'Location'), $message);
     }
 
     /**
@@ -829,17 +817,7 @@ public function assertRedirectContains($url, $message = '')
      */
     public function assertNoRedirect($message = '')
     {
-        if (!$this->_response) {
-            $this->fail('No response set, cannot assert location header. ' . $message);
-        }
-        $result = $this->_response->getHeaderLine('Location');
-        if (!$message) {
-            $message = 'Redirect header set';
-        }
-        if (!empty($result)) {
-            $message .= ': ' . $result;
-        }
-        $this->assertEmpty($result, $message);
+        $this->assertThat(null, new HeaderNotSet($this->_response, 'Location'), $message);
     }
 
     /**
@@ -852,7 +830,8 @@ public function assertNoRedirect($message = '')
      */
     public function assertHeader($header, $content, $message = '')
     {
-        $this->assertThat($content, new Header($this->_response, $header), $message);
+        $this->assertThat(null, new HeaderSet($this->_response, $header), $message);
+        $this->assertThat($content, new HeaderEquals($this->_response, $header), $message);
     }
 
     /**
@@ -865,6 +844,7 @@ public function assertHeader($header, $content, $message = '')
      */
     public function assertHeaderContains($header, $content, $message = '')
     {
+        $this->assertThat(null, new HeaderSet($this->_response, $header), $message);
         $this->assertThat($content, new HeaderContains($this->_response, $header), $message);
     }