Testing local applications is quite a challenge coz unlike other web applications they are hosted on a private IP so you can not access them in anywhere. For this you need to make a connection from your local machine to the cloud using some technique like SSH tunnel.
Tunnel makes a connection between your local machine and some cloud platform to access your locally hosted web applications on the cloud. Now the challenge that comes here is to test it for browser compatibility. For this you can connect it to a cross browser testing platform using a tunnel.
We have developed a similar feature Lambda Tunnel which allows you to test your locally hosted web applications for cross browser compatibility on over 1400 mobile and desktop configurations.
Hope this helps!