If you don’t need WebRTC, you can disable it:
In Firefox, type about:config in the URL bar then search for media.peerconnection.enabled, highlight it then right-click and select Toggle to set the Value to false
In Chrome, install the WebRTC Leak Prevent plugin by Aaron Horler and set the IP-handling policy to Disable non-proxied UDP (force proxy)
To test both browsers for IP-address leaks, use https://whoer.net