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Judging by the burrs on the inside of the piercings I would suggest it's been die-stamped - you don't get burrs like that from a piercing saw, and the ends of the cuts don't look fine enough to have been done with a saw. Perhaps it was done in the flat and then spun.
Regards, ashep. Orlrite, Trev?

Hi rat-tail. All polishing involves some degree of abrasion of the surface, and whatever you try I would strongly recommend you experiment first on a piece of scrap or something that doesn't really matter. By the sound of your Sheffield plate piece it would seem to be very tarnished and with the cop...