I was able to complete ths job today, so thanks to all who gave their
advice. As I mentioned before, the problem I was having was removing
the rusted nuts off the bolts that connect the catalytic converter and
the b pipe on my wife's 1995 Honda Accord EX. Here is how I got them
off:

1) liberal dose of PB blaster. 2) put on a small nut-cracker that I got
from Autozone for 8 or 9 bucks. I torqued the nut-cracker until the
chisel penetrated about 3/4 the way into the nut so I wouldn't hurt the
bolt. I think this process deformed the nut just enough for the PB
blaster to work its way into the threads. 3) finally, I put my ratchet
on there and the nuts broke on the second or third hit with a hammer. I
know hitting the ratchet handle with a hammer is likely to ruin the
ratchet, but I didn't have a breaker bar and the ratchet still works.

An interesting side note, it seems that the nuts are not 13mm or 14mm.
They seem to be somewhere in between, as the 13mm didn't fit over the
new replacement nuts, and the 14mm had some slop in it. I also tried
standard sockets without an exact match. Perhaps they purposely do this
so the 14mm socket will "always" fit over the nut even if it is rusted.
I guess this is a good design, especially if you are using an impact
gun.

Anyway, the job is done, and I saved myself about $100 by doing it
myself. Thanks again for everyone's input.