I made a tool for just this purpose. I mostly use it for removing stones from an old setting that I have to repair. It is made from an old dental tool. I shape the end so that it is flat with a knife edge about 1/16" wide. The shank of this end tapers up wider away from the tip. I gently work the tip between the stone and the bezel while using the wedge shape of the tool to push the bezel away from the stone. I do this all the way around and tap the back of the piece to dislodge the stone. When you push the tool in DO NOT pry the bezel away. It will tear the bezel strip especially on old pieces where the top of the bezel had worn down very thin. Let the wedge shape of the tool do the work.
Bob
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I have a very old, dull graver I use for this exact purpose, exercising the same caution about not being tempted to pry it.
BTW - I still see a really nice pendant there!
That makes a lot of sense if you need to extract stones often. I have made about 10 jewellery pieces in my life in total and out of those I had to extract 3. That’s a lot, mainly because I am stupidly impatient, but really want to get good enough not to have to do that often.
Mila
Thank you -I wish I could have saved it somehow. I loved the stone. But on the other hand, I now know what happens to a jasper when it gets cooked and it’s not pretty 
Mila