Tile saws will cut through wine bottles, with enough effort. Partly, anyway, and then you can do a controlled hammering in order to break the rest of it.

A dremel with a polishing stone will smooth out the sharp edges, and what you're left with is a vase that can hold flowers for your sweetheart - as well as something that will remind you both of that excellent vacation up to New York State's wine country.

Highly recommended: using a face mask to avoid breathing in glass dust. And sweeping up afterward.