My husband has some abrasive sheets of emery paper. He even has some on discs that he attached to his sander to polish the sink.
We have a silver metal sink that had become layered with hardened residue. It had totally lost its shine, and scrubbing with cleaners didn't help much.
He spent a long time at the sink with the emery discs, and he polished it in circular motions. When he had finished, I could see the circular pattern in the metal, and it shone like it was brand new!