This is a set of soft jaws I made for my vise. They are made from 1 x 2 inch furring strips.
A few weeks ago I was watching the Woodsmith Shop TV show
on PBS. They showed a set of homemade soft jaws for a vise held in place by magnets. That set used very powerful button magnets set into the wooden jaws on the back side. Fitting the button magnets seemed like something requiring more time and precision than I wanted to devote to the project.