Car vibrates when slowing down and stopped

Catalytic converter monitors air flow so if your vehicle seems to have no issue once you are in full motion I would rule that out; unless it is making a loud exhaust noise, then it may be of concern. My first initial response would be to check your brake pads and rotors. If those all seem to be in good (non-warped) condition. You could then check your valves in the engine but this can be costly and time consuming. Sometimes once power is reduced your valves can get sticky and make your engine vibrate or pulse. Another option could be the transmission getting slow to downshift, have your rack & pinion looked at; sometimes it is just getting the transmission tightened and lubed helps out as well.