Cleaning tarnish from silver can be surprisingly quick and easy, with no abrasives involved.
This works well for silver jewelry and coins.
To do this, you need some aluminum, baking soda, salt, hot water, and some tarnished silver.
The aluminum could be an aluminum pan, or aluminum foil.
The silver item(s) must contact both the aluminum and the baking soda solute. The tarnish is removed by converting the silver oxide back to silver. This is probably nicer than polishing, especially for coins and fine jewelry, because it doesn't remove silver, it restores it.
If you haven't seen this happen, try it. You need warm water in an aluminum pan, or a pan or baking dish lined with aluminum foil. Add a tablespoon of baking soda and a pinch of salt. When that's dissolved, place silver item(s) in good contact with the aluminum, and fully submerged in the solution. Wait about two minutes. Possibly turn the items over.
Watching the tarnish disappear seems like magic, but it's just chemistry. The tarnish oxidation is drawn to the aluminum. Clean silver is left behind.
NOTE: There are many jewelry stones that should not be treated this way, such as opals, pearls, turquoise, coral, lapis lazuli, and amber. Most hard precious stones should be OK with this.
Don't leave the items in the solution for more than 4 or 5 minutes. This works quickly, within 2 or 3 minutes. If it doesn't, then try soaking the item in a soap solution, rinse well and do it again.