diff --git a/src/browser-polyfill.js b/src/browser-polyfill.js
index a1d43ea..3ece627 100644
--- a/src/browser-polyfill.js
+++ b/src/browser-polyfill.js
@@ -95,7 +95,7 @@ if (typeof browser === "undefined" || Object.getPrototypeOf(browser) !== Object.
     const makeCallback = (promise, metadata) => {
       return (...callbackArgs) => {
         if (extensionAPIs.runtime.lastError) {
-          promise.reject(extensionAPIs.runtime.lastError);
+          promise.reject(new Error(extensionAPIs.runtime.lastError.message));
         } else if (metadata.singleCallbackArg ||
                    (callbackArgs.length <= 1 && metadata.singleCallbackArg !== false)) {
           promise.resolve(callbackArgs[0]);
@@ -484,7 +484,7 @@ if (typeof browser === "undefined" || Object.getPrototypeOf(browser) !== Object.
         if (extensionAPIs.runtime.lastError.message === CHROME_SEND_MESSAGE_CALLBACK_NO_RESPONSE_MESSAGE) {
           resolve();
         } else {
-          reject(extensionAPIs.runtime.lastError);
+          reject(new Error(extensionAPIs.runtime.lastError.message));
         }
       } else if (reply && reply.__mozWebExtensionPolyfillReject__) {
         // Convert back the JSON representation of the error into
diff --git a/test/fixtures/detect-existing-browser-api-object/content.js b/test/fixtures/detect-existing-browser-api-object/content.js
index d01a83e..016459f 100644
--- a/test/fixtures/detect-existing-browser-api-object/content.js
+++ b/test/fixtures/detect-existing-browser-api-object/content.js
@@ -33,3 +33,22 @@ test("browser api object in background page", async (t) => {
     t.ok(!reply.windowBrowserIsUnchanged, "window.browser API object should have been defined by the polyfill");
   }
 });
+
+test("error types", async (t) => {
+  if (navigator.userAgent.includes("Firefox/")) {
+    try {
+      await browser.storage.sync.set({a: 'a'});
+      t.fail('It should throw when attempting to call storage.sync with a temporary addon ID');
+    } catch (error) {
+      t.equal(error.message, 'The storage API will not work with a temporary addon ID. Please add an explicit addon ID to your manifest. For more information see https://mzl.la/3lPk1aE.');
+      t.ok(error instanceof Error);
+    }
+  } else {
+    await new Promise(resolve => {
+      chrome.storage.local.set({a: 'a'.repeat(10000000)}, resolve);
+    });
+    t.ok(chrome.runtime.lastError, 'It should throw when attempting to set an object over quota');
+    t.equal(chrome.runtime.lastError.message, 'QUOTA_BYTES quota exceeded');
+    t.notOk(chrome.runtime.lastError instanceof Error);
+  }
+});
diff --git a/test/fixtures/detect-existing-browser-api-object/manifest.json b/test/fixtures/detect-existing-browser-api-object/manifest.json
index 490091a..af6f7a3 100644
--- a/test/fixtures/detect-existing-browser-api-object/manifest.json
+++ b/test/fixtures/detect-existing-browser-api-object/manifest.json
@@ -19,5 +19,7 @@
       ]
     }
   ],
-  "permissions": []
+  "permissions": [
+    "storage"
+  ]
 }
diff --git a/test/test-async-functions.js b/test/test-async-functions.js
index 3088698..c0ea823 100644
--- a/test/test-async-functions.js
+++ b/test/test-async-functions.js
@@ -1,6 +1,6 @@
 "use strict";
 
-const {deepEqual, equal, fail, ok, throws} = require("chai").assert;
+const {deepEqual, equal, fail, ok, throws, instanceOf} = require("chai").assert;
 const sinon = require("sinon");
 
 const {setupTestDOMWindow} = require("./setup");
@@ -56,7 +56,7 @@ describe("browser-polyfill", () => {
     it("rejects the returned promise if chrome.runtime.lastError is not null", () => {
       const fakeChrome = {
         runtime: {
-          lastError: new Error("fake lastError"),
+          lastError: {message: "fake lastError"},
         },
         tabs: {
           query: sinon.stub(),
@@ -70,8 +70,11 @@ describe("browser-polyfill", () => {
 
         return window.browser.tabs.query({active: true}).then(
           () => fail("Expected a rejected promise"),
-          (err) => equal(err, fakeChrome.runtime.lastError,
-                         "Got the expected error in the rejected promise")
+          (err) => {
+            instanceOf(err, window.Error, "Expected the error to be an instance of Error");
+            equal(err.message, fakeChrome.runtime.lastError.message,
+                  "Got the expected error in the rejected promise");
+          }
         );
       });
     });