How do I test Chrome Extension/Firefox WebExtension code?

Since Firefox is forcing me to, I'm rewriting my extension to use the WebExtension APIs, i.e. Chrome's Extension APIs. I want to have automated testing. So far I've tried this:

I've got a package.json so that npm will install depedencies:

{
  "name": "extension-api-tests",
  "version": "0.0.1",
  "scripts": {
    "test": "karma start"
  },
  "devDependencies": {
    "karma": "^1.3.0",
    "karma-firefox-launcher": "^1.0.0",
    "karma-mocha": "^1.3.0",
    "karma-sinon-chrome": "^0.2.0",
    "mocha": "^3.1.2",
    "sinon-chrome": "^2.1.2"
  }
}

I've got a karma.conf.js to set up that test runner:

module.exports = function(config) {
  config.set({
    frameworks: ['mocha', 'sinon-chrome'],
    files: ['test.js'],
    reporters: ['dots'],
    autoWatch: false,
    browsers: ['Firefox'],
    singleRun: true,
    concurrency: Infinity,
  });
};

And I've got basic tests:

describe('my frustration', () => {
  it('works when it uses no APIs', done => {
    done();
  });

  it('should respond to messages!', done => {
    console.log('message test starting');
    chrome.runtime.onMessage.addListener((message, sender, sendResponse) => {
      console.log('received message');
      sendResponse(true);
    });
    chrome.runtime.sendMessage({}, result => {
      console.log('received response to message');
    });
  });

  it('should open a tab!', done => {
    console.log('tab test starting');
    chrome.tabs.create({
      'active': true,
      'url': 'http://www.example.com/',
    }, tab => {
      console.log('created a tab:', tab);
      done();
    });
  });
});

This is of course a reduced test case. When I run npm test, I get (abbreviated slightly):

> extension-api-tests@0.0.1 test .../ext-test
> karma start

25 07 2017 11:57:10.395:INFO [karma]: Karma v1.7.0 server started at http://0.0.0.0:9876/
25 07 2017 11:57:10.397:INFO [launcher]: Launching browser Firefox with unlimited concurrency
25 07 2017 11:57:10.404:INFO [launcher]: Starting browser Firefox
25 07 2017 11:57:14.687:INFO [Firefox 54.0.0 (Ubuntu 0.0.0)]: Connected on socket iIjNRRQfzWj68_GNAAAA with id 42440302
.
LOG: 'message test starting'
Firefox 54.0.0 (Ubuntu 0.0.0) my frustration should respond to messages! FAILED
        Timeout of 2000ms exceeded. For async tests and hooks, ensure "done()" is called; if returning a Promise, ensure it resolves.
LOG: 'tab test starting'
Firefox 54.0.0 (Ubuntu 0.0.0) my frustration should open a tab! FAILED
        Timeout of 2000ms exceeded. For async tests and hooks, ensure "done()" is called; if returning a Promise, ensure it resolves.
Firefox 54.0.0 (Ubuntu 0.0.0): Executed 3 of 3 (2 FAILED) (3.998 secs / 4.001 secs)
npm ERR! Test failed.  See above for more details.

My tests which try to use extension APIs all fail. It does not say (e.g.) chrome.runtime is not defined, so I believe I have sinon set up. But the APIs never do anything, never work. The code I want to test is all about passing data around through these APIs (especially as messages, to cross the chrome/content boundary).