We have a bathroom in our house where the previous owners thought it would be a good idea to paint over the tile and grout with some kind of ceramic tile paint on the walls. The house was a rental for some time before we bought it, and while we don't know how long the paint was in use, it seems to be very durable.
Since we have owned the house, we have not had any issues with the paint standing up to normal use and cleaning. We have not hit it with abrasives, but I expect it would scratch in the same ways that tile would. I haven't tested this, though. There is one spot on the wall where someone was able to cause some grief on the wall with either abrasives or some other kind of failed cleanup.
Because the paint isn't on the floor tile, it's hard to say how well it would stand up to foot traffic, but it does seem durable. On the walls in the shower, it has cracked a bit when some remodeling was done in the adjacent room (gutted kitchen to studs) and I believe there was a bit of flex in the wall during that work.
If given the choice, I'd use this kind of solution as a last resort. It doesn't look quite right and while it's durable for most instances on walls, it might not be good for floors.
If we're talking a cast iron radiator, it's a good process.
First you need to remove the old finish. You can get it sandblasted, or you can get in there with some sandpaper for a few hours. A wire wheel on an angle grinder can get out a good bit, or you might have luck with chemicals to strip them. If you do use chemicals, you'll have to wait for them to totally dry, then sand the bare metal of the radiator just to make 100% sure all of the residue is gone and the surface is rough enough.
Next, you'll want to clean with a deglosser, to make sure all the sanding residue is gone, along with any other junk in there. The paint won't bond so well without it, and with something that expands and contracts as much as a heater.. you want to make sure it's thoroughly clean.
Now it's time to protect your walls and floors. Get a drop cloth, cut a slit in it and slide it over the unit. Tape it to the walls, tape it to the floor, and tape up as much of the slit you made as you can.
You'll then need to prime it, and you'll have to chose the primer based on the paint you end up with.
Time for paint. Oil based paint should hold up, but you'll probably have better luck with spray enamel paint. Use many thin coats rather than few thick coats. Make sure to read the specs on whatever paint you decide on, make sure it can withstand up to 220 degrees - Just to be safe.
Alternatively, maybe you can look into building a radiator cover.
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I like the hardness of enamels. Oil based trim paint or the newer water borne oils are quite tough.