Run cold water on the bottle, and hot water on the stopper. Should work. Good luck.
JoanMN

You might try setting the whole thing in a bowl of cold water. Get the water up to the neck where the stopper is and see if that will release it.

Is there anyway to get a few drops of oil in the stopped area? Like baby oil or cooking oil? It might be enough to help.

I found this online:

How do you release a stuck stopper?
Hold the decanter between your knees with the stopper away from you and tap the stopper gently but repeatedly with a piece of wood (the back of an old fashioned shoe brush is ideal). The slight shock should release the stopper.
Wrap a piece of hot wet cloth round the neck of the decanter. The theory is that this will cause the glass to expand and thus release the stopper.

I hope one will help!

Oops, wrong way around! Hot water on the bottle to expand, cold water on the stopper to shrink it.

If both the bottle and stopper are glass, with no rubber or plastic, try this:

Put the bottle in a bowl of hot water; at the same time, rub an ice cube over the stopper. The bottle should expand a little, and the stopper should shrink a little.

Are you trying to save the perfume? Maybe a few minutes in the freezer would help.... or a drop of mineral oil where the 2 glass pieces meet.

And I hate to contradict Joan, but I think you would run cold on the piece you want to shrink and hot on the thing it's stuck in. If it's real dainty though, I'd be hesitant to do anything too drastic.

I obviously type way tooooo slowly! lol There was only 1 reply when I started typing. Sheesh. I edit too much.

I would go easy on the temperature extremes. If this is good glass, hot water or cold water alone can crack it--using both together is a recipe for disaster. My parents were collectors of art glass, and I can assure you that even a few degrees off of room temp can shatter some kinds of glass.

Do you have Pam cooking spray or the equivalent? Put the nozzle right up against where the stopper fits and spritz it.

I had a wine glass stuck inside a water glass and we tried hot, cold, etc., to no avail.

Pam worked!

Next time, you might try a few drops of penetrating oil.

I had an antique crystal decanter with a small quantity of homemade limoncello (50% alcohol/50% simple syrup) topped with its crystal stopper. I had it sitting in the refrigerator for two months. When I tried to open it, it was super stuck and I didn't think I would be able to get the stopper out. Tried soaking the entire bottle/stopper in a sink of hot water for 20 minutes, then took it out and the stopper started to bubble. Added a Tablespoon of olive oil and within 2 minutes, it came off. Thank you for the tips.

Debbie, even though your post is added to a seven year old thread, I think it's worth while to comment that if a piece of crystal contains lead, it should never to used to store anything.

It is well documented that lead leaches into the stored product, especially liquids.

Thank you for earlier comments - I just successfully removed a glass stopper from an antique crystal bottle by placing it in the freezer for 40 mins then turning the top clockwise - I am so grateful - Thankyou!!!