diff --git a/payment-request/rejects_if_not_active-manual.https.html b/payment-request/rejects_if_not_active-manual.https.html
index d03032d0498fc4..8e214cb6094a25 100644
--- a/payment-request/rejects_if_not_active-manual.https.html
+++ b/payment-request/rejects_if_not_active-manual.https.html
@@ -61,6 +61,8 @@
       iframe,
       "/payment-request/resources/page1.html"
     );
+    // Save the DOMException of page1.html before navigating away.
+    const frameDOMException1 = iframe.contentWindow.DOMException;
     // We navigate the iframe again, putting request1's document into an inactive state.
     const request2 = await getLoadedPaymentRequest(
       iframe,
@@ -71,6 +73,7 @@
     await promise_rejects_dom(
       t,
       "AbortError",
+      frameDOMException1,
       request1.show(),
       "Inactive document, so must throw AbortError"
     );
@@ -80,6 +83,7 @@
     await promise_rejects_dom(
       t,
       "InvalidStateError",
+      iframe.contentWindow.DOMException,
       request2.show(),
       "Abort already called, so InvalidStateError"
     );
@@ -112,6 +116,8 @@
       innerIframe,
       "/payment-request/resources/page2.html"
     );
+    // Save DOMException from innerIframe before navigating away.
+    const innerIframeDOMException = innerIframe.contentWindow.DOMException;
 
     // Navigate the outer iframe to a new location.
     // Wait for the load event to fire.
@@ -128,6 +134,7 @@
     await promise_rejects_dom(
       t,
       "AbortError",
+      innerIframeDOMException,
       showPromise,
       "Active, but not fully active, so must throw AbortError"
     );
diff --git a/resources/testharness.js b/resources/testharness.js
index 0ec232c1d27d79..4089c20c061c0e 100644
--- a/resources/testharness.js
+++ b/resources/testharness.js
@@ -638,11 +638,37 @@ policies and contribution forms [3].
         });
     }
 
+    /**
+     * Make a copy of a Promise in the current realm.
+     *
+     * @param {Promise} promise the given promise that may be from a different
+     *                          realm
+     * @returns {Promise}
+     *
+     * An arbitrary promise provided by the caller may have originated in
+     * another frame that have since navigated away, rendering the frame's
+     * document inactive. Such a promise cannot be used with `await` or
+     * Promise.resolve(), as microtasks associated with it may be prevented
+     * from being run. See https://github.com/whatwg/html/issues/5319 for a
+     * particular case.
+     *
+     * In functions we define here, there is an expectation from the caller
+     * that the promise is from the current realm, that can always be used with
+     * `await`, etc. We therefore create a new promise in this realm that
+     * inherit the value and status from the given promise.
+     */
+
+    function bring_promise_to_current_realm(promise) {
+        return new Promise(promise.then.bind(promise));
+    }
+
     function promise_rejects_js(test, constructor, promise, description) {
-        return promise.then(test.unreached_func("Should have rejected: " + description)).catch(function(e) {
-            assert_throws_js_impl(constructor, function() { throw e },
-                                  description, "promise_rejects_js");
-        });
+        return bring_promise_to_current_realm(promise)
+            .then(test.unreached_func("Should have rejected: " + description))
+            .catch(function(e) {
+                assert_throws_js_impl(constructor, function() { throw e },
+                                      description, "promise_rejects_js");
+            });
     }
 
     /**
@@ -678,17 +704,21 @@ policies and contribution forms [3].
             assert(maybeDescription === undefined,
                    "Too many args pased to no-constructor version of promise_rejects_dom");
         }
-        return promise.then(test.unreached_func("Should have rejected: " + description)).catch(function(e) {
-            assert_throws_dom_impl(type, function() { throw e }, description,
-                                   "promise_rejects_dom", constructor);
-        });
+        return bring_promise_to_current_realm(promise)
+            .then(test.unreached_func("Should have rejected: " + description))
+            .catch(function(e) {
+                assert_throws_dom_impl(type, function() { throw e }, description,
+                                       "promise_rejects_dom", constructor);
+            });
     }
 
     function promise_rejects_exactly(test, exception, promise, description) {
-        return promise.then(test.unreached_func("Should have rejected: " + description)).catch(function(e) {
-            assert_throws_exactly_impl(exception, function() { throw e },
-                                       description, "promise_rejects_exactly");
-        });
+        return bring_promise_to_current_realm(promise)
+            .then(test.unreached_func("Should have rejected: " + description))
+            .catch(function(e) {
+                assert_throws_exactly_impl(exception, function() { throw e },
+                                           description, "promise_rejects_exactly");
+            });
     }
 
     /**
diff --git a/wake-lock/wakelock-active-document.https.window.js b/wake-lock/wakelock-active-document.https.window.js
index 53f9fb56fa8d77..53745ea3c60e73 100644
--- a/wake-lock/wakelock-active-document.https.window.js
+++ b/wake-lock/wakelock-active-document.https.window.js
@@ -20,6 +20,8 @@ promise_test(async t => {
     iframe,
     "/wake-lock/resources/page1.html"
   );
+  // Save the DOMException of page1.html before navigating away.
+  const frameDOMException1 = iframe.contentWindow.DOMException;
   // We navigate the iframe again, putting wakeLock1's document into an inactive state.
   const wakeLock2 = await getWakeLockObject(
     iframe,
@@ -30,6 +32,7 @@ promise_test(async t => {
   await promise_rejects_dom(
     t,
     "NotAllowedError",
+    frameDOMException1,
     wakeLock1.request('screen'),
     "Inactive document, so must throw NotAllowedError"
   );
@@ -58,6 +61,8 @@ promise_test(async t => {
     innerIframe,
     "/wake-lock/resources/page2.html"
   );
+  // Save DOMException from innerIframe before navigating away.
+  const innerIframeDOMException = innerIframe.contentWindow.DOMException;
 
   // Navigate the outer iframe to a new location.
   // Wait for the load event to fire.
@@ -73,6 +78,7 @@ promise_test(async t => {
   await promise_rejects_dom(
     t,
     "NotAllowedError",
+    innerIframeDOMException,
     wakeLock.request('screen'),
     "Active, but not fully active, so must throw NotAllowedError"
   );