I have a 96 Honda Civic HX. When I am at idle the car starts to shake and the rpms fall almost to zero. I took the car to a mechanic and was told that I need a new Catalytic Converter and the EGR ports cleaned. Is this the reason why I have idle trouble or is it something unrelated?

Yes and No. The EGR can cause the car to idle rough and or stall. I am assumeing the check engine light was on and set code for EGR and Catalytic Converter. If the engine isn't running right it is possible the cat won't work right due to improper air fuel ratio that the EGR is causing. To do repair proper the EGR should be fixed then clear codes and see if the code for Catalytic Converter. There are other reasons that would your car to idle rough or stall I am just assuming that this mechanic got codes or tested the EGR right.