Ok, for you NON-alcoholics, I've tried a couple of the teetotaler suggestions on my ER, and they are incredibly effective!
First, I remembered that we had a proxy dental brush here in the house. So I soaked my ER for a few minutes in jewelry cleaner, brushed the outer surfaces of the diamonds with a little brush, then tried the proxy brush. I was able to get right through the metalwork on the ring and to the undersides of the diamonds. It worked great. Although, I do try to be very careful about poking the brush through the openings in the ring because I'm afraid that I'll scratch the platinum with the metal spine of the brush. But, those naughty little side pears get a VERY GOOD cleaning every time, and I CAN see a difference.
Then, just for fun, I went and got some of the denture cleanser. I sprayed on the cleanser, scrubbed the same way with the little brush, then the undersides with the proxy brush, rinsed in water, then dunked and swished in jewelry cleaner, and rubbed the ring dry with a lintless cloth (I find if I rinse in water after the cleaner, I get water spots, so I dry right from the jewelry cleaner). I must say, the denture cleaner works GREAT! My naughty pears look even MORE mirror-like. And, even if you don't notice a significant difference, it is worth it for the minty fresh scent you'll wear on your hand! Also, I'm thinking the denture cleaner is easy to pack and use when traveling.
Now, you must realize that I've become so obsessed with clean jewelry that, if necessary, I'll clean my ER, which I do wear 24/7, several times on any one day. *sigh* I may have to splurge on a Jewel Jet and an ionic cleaner.