I wanted to clean an old diamond bracelet and didn't want to use harsh chemicals, so knowing I needed to get rid of the dirt and grease, I tried Sticky Stuff Remover by De-Solv-It and I'm delighted to say it looks like new.
I soaked it for 3 mins, washed it in warm water with a little washing up liquid then buffed with a lint free cloth. No scrubbing needed. The jewellery came up really clean and very shiny. You can keep the Sticky Stuff Remover you used in a screw top jar and use it over again.
I've never seen this tip anywhere else and I have looked, so I thought I'd pass it on.