This is from americanmeadows.com
I've never tried it, but it just might work. Let us know how it turns out.

It’s true that the flowers [poppies] are very fleeting, lasting in a vase sometimes only for hours. They don’t wilt, but the delicate petals begin to fall quickly. To avoid this, there is something you can do. As you cut the flowers, take only the freshest. Then use a large match or cigarette lighter, holding the cut end of the stem over the flame, and let it sear the end of the stem until it’s almost black. This seals the milky juices into the stem, and usually at least doubles the life of the flower in water.
If you had a water pick to stick the stem into, you might get by without searing the end of the stem.