Susan Gallatin: I have used a soft toothbrush with baking soda. This seems to remove a good portion of it without damaging anything else. 
 

Kathleen Finderson (Glitter-Gals): Here are the 3 best methods of removing green gunk

1. Salt and lemon juice. Make a thin paste, apply with a brush or swab, wait 10 minutes or so, rinse or wipe off. Repeat if needed.

2. Ketchup. Yep, it really works, even tho' it looks horrible. The green gunk sort of leaves the metal and clings onto the ketchup. It is messy, but I cleaned a gorgeous Victorian expansion bracelet with it, and you can't tell where it was damaged.

3. Riceez. Love it or hate it, it really works like a charm on that horrible corrosion, and seems not to damage anything else. I cleaned a beautiful Czech necklace whose enameling and stones were almost completely obscured with mountains of ugly green stuff. You do have to clean it off again very carefully (rinsing and using a soft brush or swab works best) and dry COMPLETELY.
 

Beth (Emerald City Vintage Costume Jewelry): Baking soda is ideal for polishing off verdigris (aka green gunk). My understanding is that the only way to stop the corrosion process is to use some form of acid -- catsup, mild vinegar solution or (my favorite) lemon juice. I have a bottle of reconstituted lemon juice always at the ready in my frig. ;-) Yet - since baking soda is a buffer, able to neutralize acid or alkali, I wonder if it might not work to halt the corrosion.