home remedies to cleaning my engagement ring?

The stem to hold the diamond on my engagement ring is always getting dirty in between the nooks and crannies! I hardly ever take it off, unless I’m retaining water and get all swollen!lol! But it’s usually on. What is an easy,harmless way to clean it without having to go get it professionally cleaned? Any answers are appreciated! thanx…

My fiancee has much the same problem with her engagement ring, and after trying everything from toothbrushes to somewhat spendy silver cleaner, she ordered a cheap (<$30) ultrasonic jewelery cleaner that uses plain tap water to clean jewelery. It works remarkably well, we just drop her ring in there, hit the button and let it run for 15 minutes or so, and everything comes out looking like new.

This is the model we have:

http://www.amazon.com/Professional-Ultrasonic-Jewelry-Eyeglass-Cleaning/dp/B001DKDAVW/ref=sr_1_2?ie=UTF8&s=miscellaneous&qid=1255581923&sr=8-2