It's really easy to dent, scratch or otherwise ruin the finish on painted or plated parts when clamping them in a vise. Unfortunately, sometimes a part needs to be clamped rigidly in place to attach brackets, loosen tight fasteners or do some gentle filing. Doing this without damaging the finish is tricky, to say the least. Of course, there are alternatives to deal with this problem, herewith.
Option 1: vise manufacturers offer vinyl or rubber "booties" that fit over the jaws, of course, but we've found these things to be somewhat problematic. They often won't hold the part tight enough until the jaws are clamped hard, resulting in them scuffing the finish themselves. Also, little shreds of metal get imbedded in them. These eventually find their way to the surface and scratch the part you're trying to keep nice. They also are easy to misplace.
Here's another option: we've created wood "jaw shields" for the nine (that's right!) vises here at the Second Chance Garage. These are 1/2 inch plywood pieces cut the width of the jaws and long enough to create a U-shaped opening at the bottom. This opening acts as a saddle over the vise's main shaft and holds the wood in place. Over the years these wood shields have served well, but they do eventually crack and get dirty or greasy. When that happens they don't hold shiny parts well.
So what's the best solution? Well, this is one of those situations where the best solution is also the cheapest. Got an old belt, leather briefcase or pair of boots? Don't throw away that thick leather. Cut it in pieces large enough to cover the vise jaws and keep it handy. When you have a delicate part to clamp, either wrap it in the leather or, if too large, place the leather scraps between the jaws and the piece. It holds great, doesn't mar shiny finishes and stays reasonably clean.
Try it sometime. It works great!