Sandpaper of increasing fineness.

And patience. Lots of patience.

How did you hold the items securely while sanding them down? Standard hand vices or some kind of custom jigs?

Not my project, but embedding the part in a plug of epoxy would make it easier to handle.

we used a variety of tools: diamond saws, polishing wheels, hacksaws, and a lot of sandpaper.

many of the samples had to be mounted using clamps or dop wax.