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I use Mothers Chrome Cleaner and Polish. Removes all the dirt, grime and soot build up and leaves the tips looking like chrome. Then when polishing the car (I use Zaino) the last thing I do with whatever Zaino I have left is to use that on the tips. Been using these products since 1999 and I see no reason to change.
AFVette's method is very good. You can also use other metal cleaners like Flitz, etc if you have them.
I find the best and quickest maintenance is to wipe them clean with a diaper or other soft thick cloth (so you dont burn your hand) when you are done driving or while they are still warm (credit goes to Pipedreams on this one).
If the metal has Zaino (or Rejex, or Mothers, etc) on it, the moist carbon wipes off easily then, and pipes stay cleaner longer without the need for frequent polishing.
After I wash and dry the car, including the chrome tips, I use slightly damp (followed by dry) paper towels to clean the soot from the inside of the chrome tips. Once in a while, I also use an automotive chrome polish....both on the inside and outside of the chrome tips.
Mother's has a Mag & Aluminum polish that is safe for all metals except chrome. I used to use it on my stainless steel tips with good results before I switched to chrome tips, now I use Mother's Chrome Polish instead.
I use my pneumatic 3-1/2" polisher with foam pad and 3M polish. Perfect fit for the tips and takes all the work out of it. They look brand new every day.