We often store herbs this way, like flowers in a vase, in our refrigerator. The problem is that, too often, the glass is too big for a small bunch, and many of the leaves get submerged and slimy. Enter a random shot glass we had lying around...The stems of our cilantro stay fresh and hydrated, but the leaves are free and fluffy. We like this method of storing herbs, as opposed to wrapping them in a damp paper towel and putting them in a plastic bag, simply because they are front and center in the fridge (not hidden in a drawer) and we don't forget to use them.
Any other tips out there?