The Cisco Meeting web app does not support testing camera and microphone.
However, the browser web app uses the webRTC technology, and there is a tool you can use to test your browser's webRTC support.
For Google Chrome, go to https://apprtc.appspot.com using Chrome. If you see a self-view this validates that Chrome can access your camera and microphone, and that a call should generally work.
Then copy and send the link shown at the bottom to someone and initiate a point-to-point call with live two-way audio and video.
Success of these tests indicates that WebRTC calls with the Meeting Server should also be successful − if you have the same firewall configurations between the Meeting Server and the browser as you do between the two browsers in the call.