--- a/toolkit/components/remotebrowserutils/tests/browser/browser_RemoteWebNavigation.js
+++ b/toolkit/components/remotebrowserutils/tests/browser/browser_RemoteWebNavigation.js
@@ -1,27 +1,19 @@
-var { interfaces: Ci, classes: Cc, utils: Cu, results: Cr } = Components;
+/* eslint-env mozilla/frame-script */
 
 const DUMMY1 = "http://example.com/browser/toolkit/modules/tests/browser/dummy_page.html";
 const DUMMY2 = "http://example.org/browser/toolkit/modules/tests/browser/dummy_page.html"
 
 function waitForLoad(browser = gBrowser.selectedBrowser) {
-  return new Promise(resolve => {
-    browser.addEventListener("load", function() {
-      resolve();
-    }, {capture: true, once: true});
-  });
+  return BrowserTestUtils.browserLoaded(browser);
 }
 
 function waitForPageShow(browser = gBrowser.selectedBrowser) {
-  return new Promise(resolve => {
-    browser.addEventListener("pageshow", function() {
-      resolve();
-    }, {capture: true, once: true});
-  });
+  return BrowserTestUtils.waitForContentEvent(browser, "pageshow", true);
 }
 
 function makeURI(url) {
   return Cc["@mozilla.org/network/io-service;1"].
          getService(Ci.nsIIOService).
          newURI(url);
 }
 
@@ -30,93 +22,109 @@ add_task(function* test_referrer() {
   gBrowser.selectedTab = gBrowser.addTab();
   let browser = gBrowser.selectedBrowser;
 
   browser.webNavigation.loadURI(DUMMY1,
                                 Ci.nsIWebNavigation.LOAD_FLAGS_NONE,
                                 makeURI(DUMMY2),
                                 null, null);
   yield waitForLoad();
-  is(browser.contentWindow.location, DUMMY1, "Should have loaded the right URL");
-  is(browser.contentDocument.referrer, DUMMY2, "Should have the right referrer");
+
+  yield ContentTask.spawn(browser, [ DUMMY1, DUMMY2 ], function([dummy1, dummy2]) {
+    is(content.location, dummy1, "Should have loaded the right URL");
+    is(content.document.referrer, dummy2, "Should have the right referrer");
+  });
 
   gBrowser.removeCurrentTab();
 });
 
 // Tests that remote access to webnavigation.sessionHistory works.
 add_task(function* test_history() {
+  function checkHistoryIndex(browser, n) {
+    return ContentTask.spawn(browser, n, function(n) {
+      let history = docShell.QueryInterface(Ci.nsIInterfaceRequestor)
+                            .getInterface(Ci.nsISHistory);
+      is(history.index, n, "Should be at the right place in history");
+    });
+  }
   gBrowser.selectedTab = gBrowser.addTab();
   let browser = gBrowser.selectedBrowser;
 
   browser.webNavigation.loadURI(DUMMY1,
                                 Ci.nsIWebNavigation.LOAD_FLAGS_NONE,
                                 null, null, null);
   yield waitForLoad();
 
   browser.webNavigation.loadURI(DUMMY2,
                                 Ci.nsIWebNavigation.LOAD_FLAGS_NONE,
                                 null, null, null);
   yield waitForLoad();
 
-  let history = browser.webNavigation.sessionHistory;
-  is(history.count, 2, "Should be two history items");
-  is(history.index, 1, "Should be at the right place in history");
-  let entry = history.getEntryAtIndex(0, false);
-  is(entry.URI.spec, DUMMY1, "Should have the right history entry");
-  entry = history.getEntryAtIndex(1, false);
-  is(entry.URI.spec, DUMMY2, "Should have the right history entry");
+  yield ContentTask.spawn(browser, [DUMMY1, DUMMY2], function([dummy1, dummy2]) {
+    let history = docShell.QueryInterface(Ci.nsIInterfaceRequestor)
+                          .getInterface(Ci.nsISHistory);
+    is(history.count, 2, "Should be two history items");
+    is(history.index, 1, "Should be at the right place in history");
+    let entry = history.getEntryAtIndex(0, false);
+    is(entry.URI.spec, dummy1, "Should have the right history entry");
+    entry = history.getEntryAtIndex(1, false);
+    is(entry.URI.spec, dummy2, "Should have the right history entry");
+  });
 
   let promise = waitForPageShow();
   browser.webNavigation.goBack();
   yield promise;
-  is(history.index, 0, "Should be at the right place in history");
+  yield checkHistoryIndex(browser, 0);
 
   promise = waitForPageShow();
   browser.webNavigation.goForward();
   yield promise;
-  is(history.index, 1, "Should be at the right place in history");
+  yield checkHistoryIndex(browser, 1);
 
   promise = waitForPageShow();
   browser.webNavigation.gotoIndex(0);
   yield promise;
-  is(history.index, 0, "Should be at the right place in history");
+  yield checkHistoryIndex(browser, 0);
 
   gBrowser.removeCurrentTab();
 });
 
 // Tests that load flags are passed through to the content process.
 add_task(function* test_flags() {
+  function checkHistory(browser, { count, index }) {
+    return ContentTask.spawn(browser, [ DUMMY2, count, index ],
+      function([ dummy2, count, index ]) {
+        let history = docShell.QueryInterface(Ci.nsIInterfaceRequestor)
+                              .getInterface(Ci.nsISHistory);
+        is(history.count, count, "Should be one history item");
+        is(history.index, index, "Should be at the right place in history");
+        let entry = history.getEntryAtIndex(index, false);
+        is(entry.URI.spec, dummy2, "Should have the right history entry");
+      });
+  }
+
   gBrowser.selectedTab = gBrowser.addTab();
   let browser = gBrowser.selectedBrowser;
 
   browser.webNavigation.loadURI(DUMMY1,
                                 Ci.nsIWebNavigation.LOAD_FLAGS_NONE,
                                 null, null, null);
   yield waitForLoad();
 
   browser.webNavigation.loadURI(DUMMY2,
                                 Ci.nsIWebNavigation.LOAD_FLAGS_REPLACE_HISTORY,
                                 null, null, null);
   yield waitForLoad();
-
-  let history = browser.webNavigation.sessionHistory;
-  is(history.count, 1, "Should be one history item");
-  is(history.index, 0, "Should be at the right place in history");
-  let entry = history.getEntryAtIndex(0, false);
-  is(entry.URI.spec, DUMMY2, "Should have the right history entry");
+  yield checkHistory(browser, { count: 1, index: 0 });
 
   browser.webNavigation.loadURI(DUMMY1,
                                 Ci.nsIWebNavigation.LOAD_FLAGS_BYPASS_HISTORY,
                                 null, null, null);
   yield waitForLoad();
-
-  is(history.count, 1, "Should still be one history item");
-  is(history.index, 0, "Should be at the right place in history");
-  entry = history.getEntryAtIndex(0, false);
-  is(entry.URI.spec, DUMMY2, "Should have the right history entry");
+  yield checkHistory(browser, { count: 1, index: 0 });
 
   gBrowser.removeCurrentTab();
 });
 
 // Tests that attempts to use unsupported arguments throw an exception.
 add_task(function* test_badarguments() {
   if (!gMultiProcessBrowser)
     return;