I will start this by saying that I am most familier with the requirements for european CE marking.
It is possible to do a certain amount of pre-testing to see if your product has any problems. The easiest way would be with a spectrum analyser and probes. However, you would probably not be able to use this as proof of compliance as this would be mostly detecting near field signals not far field signals. It will give you some idea if your product has any potential emission problems.
Also, depending on what the product is, some tests might require equipment that is large or dangerous. You might be able to hire this but the costs would quickly out weigh any savings. For example if your product is mains powered you might have to test the following:
1. Mains surges the level of which depends on input voltage but could easily be a 3kV spike. In order to do this test the tester must be attached to a supply with a very low impedance.
2. Conducted Emissions (the noise the product outputs down the mains)
3. Burst. (High frequency repeating spikes that can upset some electronics)
4. Electrostatic discharge to the mains plug / input socket.
5. Conducted Immunity (how the product reacts to noise <30MHz on the mains)
6. Harmonic emissions (another measure of output noise.)
7. Voltage brownouts / blackouts.
8. Flicker tests (see if the product could cause the lights to flicker)
Those are the tests I know about - we have a test lab at work and we have the equipment to do these tests. Given that many of these can broadcast noise and cause interference they are done in a special shielded room.
The one advantage of a test house is that they will be experienced in interpreting the standards you have to meet. For instance it is possible that there are several different standards that could be applied - they will be able to help with the correct standard. Also, should you have problems with passing the experience of the technicians will be invaluable to help suggest possible cures.
If this has not detered you, I would suggest going to
http://www.compliance-club.com/ and looking through that - I know that there are some links to how to do some of these test.
Yours
Neil