The catalytic converters per se won't be throwing a code since there's no directly sensor for the converter. But the oxygen sensors either before or after the converters might be registering values that suggest there could be an issue with a converter. There are a lot of folks on this forum that are pretty familiar with the typical codes, and a lot of codes related to catalytic converters that could be caused by something other than a bad converter. Granted, having a bad cylinder that was either letting oil past the rings and into the exhaust or misfiring and passing fuel into the exhaust could lead to a catalytic converter failing, there could be other much less expensive causes for some codes related to the converter that might also be worth exploring first.
It may be in your wallet's best interest to share the exact codes that your car has and let the community guide you on their experience with the code/codes as well as replacement catalytic converter options.
-Rod