Esentially what your looking for is a restriction in the exhaust system.
you did not mention what type of car that you had,,The first thing that would give you an indication of a restricted exhaust system is a loss of power,,this could include a rough idle and or stalling. When the engine is idling can you hear a rattling noise coming from exhaust system ? Can you smell exhaust vapors anywhere along the piping ? Where there are connections between the cat and the muffler is there evidence of black soot ? When you "rev up " the engine exhaust gasses being expelled from the tail pipe should increase. Older cars and trucks that used an air pump the dicharged air in to a fitting on the exhaust manifold allowed the mechanic to to remove the check valve and when they reved up the engine and if a lot of exhaust gas pressure came out of the fitting then this was a good indication that there was a restriction.
You may need to remove the components and physically check the muffler and the cat(s) seperately,,When you remove the cat if any material falls out, there is a rattling sound when you shake it, you cant see a flashlight thru it, or it looks clogged you will need to replace it, The same basicly goes for the muffler except for the flashlight part. On a well maintained car/truck these parts should last about between 7-12 yrs +/- .
I agree with bandit that the first thing you should check for is any stored codes as for replacing anything with the exhaust system could run you from $ 100.00 To well over several thousand dollars,,depending on the year,,make and model of your vehicle.