The following are photos showing how I removed a glass stopper from a perfume bottle.
1) The problem: The bottle and the stopper are made from glass, which is fragile. The stopper and the spout are tapered, which means they can easily seize together and get stuck. If a stuck stopper is twisted, it can easily snap off, as in the picture below. If you have worked with stuck tapers you know that they come apart best when pulled directly out. But in this case there was nothing grab onto to do that.
2) The solution: I drilled a hole in the stopper and epoxied a nail in the hole. See pictures below.
I used a 1/8″ diamond drill (from Harbor Freight) in my drill press. It is important to keep everything as rigid as possible so the drill can move directly up and down with no side play. I used plastiline clay to hold the bottle in place and to make a dam for keeping water around drill, to keep it from overheating. I drilled into the glass about 3/16″.
I used Devcon 5 minute epxoy to glue a small nail (with a head — important) into the hole and let it cure overnight.
5 minute epoxy is very strong — except when hot. I carefully heated the nail, keeping the heat away from the glass, until I could feel the nail loosening, then I twisted it out. Then I used a small screwdriver to completely scrape and clean the old epoxy out of the hole.
I buffed the finial, washed it, blew the hole out with an air gun, degreased it with lacquer thinner and used 5 minute epoxy to glue the stopper onto the finial. I used a thin metal poker to work the epoxy into the hole I drilled for the nail, which also served to anchor the stopper better. The iron jig helped me align everything by rotating it so I could see (and correct) any wobble.