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.
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.
If it does not work, ask your administrator to help investigate.