I do these kind of cutouts at work all the time, albeit from brass mostly, and thin aluminium...2-3mm max. What I do is, get a roll of 300mm wide application tape (the stuff used for vinyl graphics). Put a layer of this on the back of your sheet of material. Use a backing sheet for the bed of the machine (I usually just use 2mm acrylic or similar) and put a layer of the app tape on that also. Stick the 2 sheets together tape to tape with double sided tape, and clamp that on the bed of your machine. Should stay solid as a rock and not move around when cutting.
On a side note, I also do pewter casting and could possibly make some of these in an antique pewter if we can get a prototype to make a mold from.