A couple of weeks ago I had to shoot a presentation for a speaker and had just enough set-up time for a couple of cameras and an HD Tricaster to switch between them. There was very little light in the room and the projector was directly behind the speaker--. a "worst-case scenario" because of its brightness and color temperature difference, but one in which we seem to find ourselves quite often. My only option was to underexpose the scene, putting the whites of the screen just into the clipping range and letting the darks, including the speaker, fall where they may. I knew that there would be some graininess in my final product, but I did the best I could.
Fortunately, there are some handy ways of correcting levels in post production, and some are included already in editing software packages. The go-to correction controls are the three-way color correction filters that allow you to adjust the bright, dark, and mid tones separately. This means you can bring the brightness of the screen down without adjusting the blacks at all, and you can bring the dark areas up without pushing the bright areas to where they clip. With these controls, you can even out a contrasty shot like you see on the left (the original shot). There are other plug-ins for this, too. On this shot I actually used one of my favorites--the free Shadow-Highlight plug-in for Final Cut Pro from Lyric. In about five seconds, I was able to correct my blown out highlights and bring the shadow areas up to where the speaker is visible. While I would still not consider it a great-looking shot, it is a far cry from what it was.