Both pewter and silver can be truly polished in a vibratory tumbler.
The finish can be every bit as good as you can do by hand. That
said, several steps are required.
First you do an abrasive step to remove surface roughness, then if
the items are textured a burnishing step with steel or ceramic beads.
For items that are quite smooth, I omit the burnishing step and run
them instead in a mixture of wood chips and wood pegs charged with
simichrome or chrome oxide. Voila, perfecto!
And just a comment on using regular soap rather than the prepared
chemicals, it kinda works - but the stuff made for the process works
far better. It is not only a lubricant, it also has surficants, and
is the appropriate pH for the media. You get a better result in my
Judy Hoch, G.G. @Judy_Hoch www.marstal.com