I had an accident on my carbon road bike. As I look at it, I do not see visible damage to the frame or forks. Is there a way that the frame can be tested for damage and if so, how do I get this testing done?
I've heard of people having their frames x-rayed, but for obvious reasons that's not very practical. The most reliable manner of checking a carbon frame for damage that I'm aware of is the old coin tap test. Get a quarter ( or whatever coin fits that form factor in your local currency) and go over the frame lightly tapping the edge of the coin against the frame. Intact carbon makes a distinct "clack", whereas damaged, delaminating carbon will have a much duller thud sound when tapped. Keep in mind that as the tubes change shapes and thicknesses the sound will gradually change. What you're looking for is a distinctly different muted report that abruptly changes within a very localized area. Keep in mind that this is not a foolproof or exhaustive method of checking your frame and fork for damage, but it does work surprisingly well. I've found many a damaged frame this way.
In recent years more specialty shops that deal in carbon frame repair have become more available. Many are shops that do custom frame builds. A Google search may get some leads that are local thus savings on shipping. In the Northeast U.S. I have used HotTubes.com to check a frame. I was reluctant to go to my local bike shop due to the limited number of frames they see per year. In addition to the fact that they couldn't do any repairs if they were needed. As @jm2 has stated nothing is foolproof. However the replacement cost of the frame and the risk involved of riding with a damaged frame would make spending a couple hundred dollars for an inspection or repair a viable investment.