Most of us made our own barrel vise jaws.

These can be machined from aluminum or one of the glass filled hard plastics.

Good ones can be made from hard oak and epoxy by casting 1/2 of a jaw on the barrel, then casting the other half.
When on the barrel you want a gap between the jaws so they'll clamp tightly to the barrel. When tightened in the vise you want about 1/8th of an inch gap.

After making, use paint thinner to clean off all release agent and keep them in a clean plastic bag.
Never allow them to lay around on the bench, and both before and after using clean them carefully.
Any grit or dirt that gets inside will scar the barrel.

I modified the jaws of a shop vise to hold the barrel vise jaws.

For old type round barrels I used a small version of a rifle barrel vise using a small hydraulic jack, and either oak blocks or brass rings to clamp around the barrel.
It's critical that round barrels be clamped very tightly.
If the set up isn't tight enough the barrel will turn in the jaws and that will strip the finish right off.