On black I would use all purpose cleaner/degreaser.
Have you heard of 'Bar Keepers Friend' - that stuff is brilliant, I use it on the oven and the oven door.
I have the one that comes in a powder, then you add a bit of water to make a smooth paste and leave it on for a bit.
(you can get it from Wilko/Lakeland/The Range etc)
Chromed tips, I use the Britemax Metal Twin polishes, the cleaner/polish #1, then the sealant/finish #2.
For about £14 they will sort out any metal you throw at them.
Whatever you do, and whatever you have, I'd recommend cleaning with IPA or Panel Wipe, then apply a coat of high temperature wax or sealant such as Gtechniqs brilliant C5 armour (which is actually for wheels) The melting point of that coating is about 350degC
I coated my genuine twin sports tailpipe with C5 and they're still like new after nearly a year.