Normally the sessions of United States congress are available online for review by the public. Are the session(s) which involve the certification of the results of the US Presidential Elections (of 2012) available online? What day was the session held? Which of the two bodies certified it? (I believe its a joint session of the committee of the whole, but I'm not sure.)
This C-Span link shows the Electoral College certifying the results, on December 17th, in accordance with the Constitution.
The Congressional Session approving the results of the Electoral College will occur on January 6, 2013. See here. This answer was written on January 2, and as such, it has not yet occurred.
To see the actual casting of ballots, you would need to locate the live feeds of each state's legislature, and as they needed to have met by December 17. States such as mine have already thus cast their ballots, but they have not yet been counted. C-Span, a staple on many basic cable channels, is sure to carry it.
If you are wondering why it is so "late," remember that Inauguration Day was, until the 20th amendment, March 4th. This lame duck period was necessarily long in order to both ensure time for a transition, and to allow for travel from far flung states to Washington, DC. Just think how long it took to get from New Hampshire or Atlanta to DC on horseback.