The answer here is tesselation, if I understand your question correctly. While it's very difficult to get great results, good ones are not impossible. Here's a few suggestions:
Wherever possible, rebuild. I don't mean the auto-rebuild surface tool, I mean use the trim, the fillet or the intersect tool to define your curves, then use birail, square or other tools to create non-trimmed surfaces.
If that's impossible, turn on the hardware shaded mode and display the render tesselation in your attribute editor. There, adjust the values so that the tesselation matches as closely as possible. Remember, the key here is that the triangles line up with each other, not that you have more triangles. Sometimes fewer are better. Often, I have not had to turn on the advanced tesselation options; I've gotten good results with just the curvature tolerance and the U and V divisions factors. Get to know what all the tesselation attributes mean, and resist the temptation to just crank them all up and hope for the best.
Finally, I think you can get better results if you build your object large and scale it down after the trim. Although I haven't really "formally" investigated this, I think it has something to do with how accurately Maya is able to calculate larger radii on fillets.
Hope this helps - I've been wrestling with the same problem. If anyone else has any suggestions, I would really love to hear them.