diff -u b/core/modules/system/tests/src/Functional/Update/DbUpdatesTrait.php b/core/modules/system/src/Tests/Update/DbUpdatesTrait.php
--- b/core/modules/system/tests/src/Functional/Update/DbUpdatesTrait.php
+++ b/core/modules/system/src/Tests/Update/DbUpdatesTrait.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\Tests\system\Functional\Update;
+namespace Drupal\system\Tests\Update;
 
 use Drupal\Core\StringTranslation\StringTranslationTrait;
 use Drupal\Core\Url;
@@ -9,7 +9,10 @@
  * Provides methods to conditionally enable db update functions and apply
  * pending db updates through the Update UI.
  *
- * This should be used only by classes extending \Drupal\Tests\BrowserTestBase.
+ * This should be used only by classes extending \Drupal\simpletest\WebTestBase.
+ *
+ * @deprecated in Drupal 8.4.0 and will be removed before Drupal 9.0.0.
+ *   Use \Drupal\FunctionalTests\Update\DbUpdatesTrait.
  */
 trait DbUpdatesTrait {
 
diff -u b/core/modules/system/tests/src/Functional/Update/UpdatePathRC1TestBaseFilledTest.php b/core/modules/system/tests/src/Functional/Update/UpdatePathRC1TestBaseFilledTest.php
--- b/core/modules/system/tests/src/Functional/Update/UpdatePathRC1TestBaseFilledTest.php
+++ b/core/modules/system/tests/src/Functional/Update/UpdatePathRC1TestBaseFilledTest.php
@@ -89,7 +89,7 @@
 
     // Log in as user 1.
     $account = User::load(1);
-    $account->pass_raw = 'drupal';
+    $account->passRaw = 'drupal';
     $this->drupalLogin($account);
 
     // Make sure we can see the access-restricted entity reference field
diff -u b/core/modules/system/tests/src/Functional/Update/UpdatePathTestJavaScriptTest.php b/core/modules/system/tests/src/Functional/Update/UpdatePathTestJavaScriptTest.php
--- b/core/modules/system/tests/src/Functional/Update/UpdatePathTestJavaScriptTest.php
+++ b/core/modules/system/tests/src/Functional/Update/UpdatePathTestJavaScriptTest.php
@@ -37,12 +37,12 @@
     $scripts = $this->xpath('//script');
     $found = FALSE;
     foreach ($scripts as $script) {
-      if (!isset($script['src'])) {
+      if (!$script->getAttribute('src')) {
         continue;
       }
       // Source is a root-relative URL. Transform it to an absolute URL to allow
       // file_get_contents() to access the file.
-      $src = preg_replace('#^' . $GLOBALS['base_path'] . '(.*)#i', $GLOBALS['base_url'] . '/' . '${1}', (string) $script['src']);
+      $src = preg_replace('#^' . $GLOBALS['base_path'] . '(.*)#i', $GLOBALS['base_url'] . '/' . '${1}', $script->getAttribute('src'));
       $file_content = file_get_contents($src);
 
       if (strpos($file_content, 'window.drupalSettings =') !== FALSE) {
diff -u b/core/modules/system/tests/src/Functional/Update/UpdatePathWithBrokenRoutingTest.php b/core/modules/system/tests/src/Functional/Update/UpdatePathWithBrokenRoutingTest.php
--- b/core/modules/system/tests/src/Functional/Update/UpdatePathWithBrokenRoutingTest.php
+++ b/core/modules/system/tests/src/Functional/Update/UpdatePathWithBrokenRoutingTest.php
@@ -32,16 +32,6 @@
     $this->drupalGet('<front>');
     $this->assertResponse(500);
 
-    // The exceptions are expected. Do not interpret them as a test failure.
-    // Not using File API; a potential error must trigger a PHP warning.
-    unlink(\Drupal::root() . '/' . $this->siteDirectory . '/error.log');
-    foreach ($this->assertions as $key => $assertion) {
-      if (strpos($assertion['message'], 'core/modules/system/tests/modules/update_script_test/src/PathProcessor/BrokenInboundPathProcessor.php') !== FALSE) {
-        unset($this->assertions[$key]);
-        $this->deleteAssert($assertion['message_id']);
-      }
-    }
-
     $this->runUpdates();
 
     // Remove the simulation of the broken router, and make sure we can get to
diff -u b/core/modules/system/tests/src/Functional/Update/UpdatePostUpdateFailingTest.php b/core/modules/system/tests/src/Functional/Update/UpdatePostUpdateFailingTest.php
--- b/core/modules/system/tests/src/Functional/Update/UpdatePostUpdateFailingTest.php
+++ b/core/modules/system/tests/src/Functional/Update/UpdatePostUpdateFailingTest.php
@@ -34,7 +34,7 @@
     $this->assertIdentical([], \Drupal::state()->get('post_update_test_execution', []));
 
     $key_value = \Drupal::keyValue('update__post_update');
-    $this->assertEqual([], $key_value->get('existing_updates'));
+    $this->assertEqual([], $key_value->get('existing_updates', []));
   }
 
   /**
diff -u b/core/modules/system/tests/src/Functional/Update/UpdateSchemaTest.php b/core/modules/system/tests/src/Functional/Update/UpdateSchemaTest.php
--- b/core/modules/system/tests/src/Functional/Update/UpdateSchemaTest.php
+++ b/core/modules/system/tests/src/Functional/Update/UpdateSchemaTest.php
@@ -57,6 +57,7 @@
     $this->assertRaw('Schema version 8001.');
     // Run the update hooks.
     $this->clickLink(t('Apply pending updates'));
+    $this->checkForMetaRefresh();
 
     // Ensure schema has changed.
     $this->assertEqual(drupal_get_installed_schema_version('update_test_schema', TRUE), 8001);
diff -u b/core/modules/system/tests/src/Functional/Update/UpdateScriptTest.php b/core/modules/system/tests/src/Functional/Update/UpdateScriptTest.php
--- b/core/modules/system/tests/src/Functional/Update/UpdateScriptTest.php
+++ b/core/modules/system/tests/src/Functional/Update/UpdateScriptTest.php
@@ -119,6 +119,7 @@
     $this->assertNoText('This is a requirements warning provided by the update_script_test module.');
     $this->clickLink(t('Continue'));
     $this->clickLink(t('Apply pending updates'));
+    $this->checkForMetaRefresh();
     $this->assertText(t('The update_script_test_update_8001() update was executed successfully.'), 'End of update process was reached.');
     // Confirm that all caches were cleared.
     $this->assertText(t('hook_cache_flush() invoked for update_script_test.module.'), 'Caches were cleared after resolving a requirements warning and applying updates.');
@@ -167,7 +168,7 @@
     $this->clickLink(t('Continue'));
     $this->assertText(t('No pending updates.'));
     $this->assertNoLink('Administration pages');
-    $this->assertNoLinkByHrefInMainRegion('update.php', 0);
+    $this->assertEmpty($this->xpath('//main//a[contains(@href, :href)]', [':href' => 'update.php']));
     $this->clickLink('Front page');
     $this->assertResponse(200);
 
@@ -178,7 +179,7 @@
     $this->clickLink(t('Continue'));
     $this->assertText(t('No pending updates.'));
     $this->assertLink('Administration pages');
-    $this->assertNoLinkByHrefInMainRegion('update.php', 1);
+    $this->assertEmpty($this->xpath('//main//a[contains(@href, :href)]', [':href' => 'update.php']));
     $this->clickLink('Administration pages');
     $this->assertResponse(200);
   }
@@ -209,10 +210,11 @@
     $this->drupalGet($this->updateUrl, ['external' => TRUE]);
     $this->clickLink(t('Continue'));
     $this->clickLink(t('Apply pending updates'));
+    $this->checkForMetaRefresh();
     $this->assertText('Updates were attempted.');
     $this->assertLink('logged');
     $this->assertLink('Administration pages');
-    $this->assertNoLinkByHrefInMainRegion('update.php', 1);
+    $this->assertEmpty($this->xpath('//main//a[contains(@href, :href)]', [':href' => 'update.php']));
     $this->clickLink('Administration pages');
     $this->assertResponse(200);
   }
@@ -275,10 +277,11 @@
     $this->drupalGet($this->updateUrl, ['external' => TRUE]);
     $this->clickLink(t('Continue'));
     $this->clickLink(t('Apply pending updates'));
+    $this->checkForMetaRefresh();
     $this->assertText('Updates were attempted.');
     $this->assertLink('logged');
     $this->assertLink('Administration pages');
-    $this->assertNoLinkByHrefInMainRegion('update.php', 1);
+    $this->assertEmpty($this->xpath('//main//a[contains(@href, :href)]', [':href' => 'update.php']));
     $this->clickLink('Administration pages');
     $this->assertResponse(200);
   }
@@ -306,6 +309,7 @@
     $this->drupalGet($this->updateUrl, ['external' => TRUE]);
     $this->clickLink(t('Continue'));
     $this->clickLink(t('Apply pending updates'));
+    $this->checkForMetaRefresh();
 
     // Verify that updates were completed successfully.
     $this->assertText('Updates were attempted.');
@@ -318,7 +322,7 @@
 
     // Verify that there are no links to different parts of the workflow.
     $this->assertNoLink('Administration pages');
-    $this->assertNoLinkByHrefInMainRegion('update.php', 0);
+    $this->assertEmpty($this->xpath('//main//a[contains(@href, :href)]', [':href' => 'update.php']));
     $this->assertNoLink('logged');
 
     // Verify the front page can be visited following the upgrade.
diff -u b/core/tests/Drupal/Tests/BrowserTestBase.php b/core/tests/Drupal/Tests/BrowserTestBase.php
--- b/core/tests/Drupal/Tests/BrowserTestBase.php
+++ b/core/tests/Drupal/Tests/BrowserTestBase.php
@@ -277,7 +277,7 @@
   /**
    * {@inheritdoc}
    */
-  public function __construct($name = NULL, array $data = array(), $dataName = '') {
+  public function __construct($name = NULL, array $data = [], $dataName = '') {
     parent::__construct($name, $data, $dataName);
 
     $this->root = dirname(dirname(substr(__DIR__, 0, -strlen(__NAMESPACE__))));