What's the best way to stream LIVE Video at a Conference to a Website?

This is my first post. Could someone please help me or guide me to the correct post if this has already been answered.

I videotape conferences and I have a client that wants to broadcast the LIVE video feed to their website so people can watch and listen while it is happening. I am already videotaping, so I am receiving a digital video feed with audio. I would like to use a 2nd Mac or PC to capture the video and audio for this purpose. I know there must be an easy way to do this using software. Any suggestions?

Thank you in advance,

GPVideo