Leaky vase problem  

Sounds like it is a porous ce...
Sounds like it is a porous ceramic, not intended to hold water. Clay that is fired at low heat is water permeable. You could try letting it dry out completely and then pour some polyurethane into it and swish it around to coat the inside. Let it dry and then cure for a few weeks, then test it.
Or put a silk or paper flower in it.

What she said.
Mexican pottery is low-fired too and sweats all over the place. Don't ever put it on a wood table!

I assume
that polyurethane finish, and not polyurethane glue, is what was advised. Sounds like a good idea to me. Does Koen, a professional ceramist, have any advice ?

A less invasive solution,
for a single stem, might be a small-diameter test tube secured at the lower end with a dab of wax or double-sided tape.

I would be careful..
...with anything that will be absorbed by the porous clay and could show up on the outside surface of the vase. Poly-urethane is probably safe, but I have never tried it, so I would not recommend it. The same thing of course would apply for any kind of polyester. I would always glaze the inside, no matter how low the temperature (there are glazes for as low as 850 degrees Celcius)of the firing is, but that's too late now. A collegue of mine is producing funeral urns and to avoid the problems, one can only imagine, when the urn falls during the ceremony (it happens)the urns are coated on the inside with a rubber coating that is available in most car part stores...I will try to find out

sorry...
I pushed too many keys and repeated the message