The catalytic converter has an oxygen sensor in front and behind it. When the vehicle is warm and running in closed loop mode, the upstream oxygen sensor waveform reading should fluctuate. The downstream O2 sensor reading should be fairly steady. Typically the P0420 code triggers the Check Engine Light (CEL) if the readings of the two sensors are similar. This is indicative of (among other things) a converter that is not working as efficiently as it should be (according to specs). However, it may be that the rear O2 sensor is bad and not necessarily that the cat is bad. You will not harm anything by driving the car till the engine CEL comes back, so relax about that. Now, the first thing to do if the CEL comes back on is go to your local auto parts store and have them hook up an OBDII scanner to the car and check for any fault codes. Many auto parts stores will do this for free. Confirm that you had this code. I would then go to Car Talk’s Mechanics Files site at
Enter your zip code and you will get a list of mechanics in your area that other consumers have used and highly recommend. Look for ones that specialize either in the make of your car or the type of problem you have. Call 2-3 of them and ask them for a quote on a cat replacement. I have personally used this site with great success to find good honest mechanics and can highly recommend it. Good luck!