It turns out that ceramic pots - or at least the ones I own - don't crack when you drill into the bottoms to create drainage holes, as I'd feared. That's excellent news, because my plants are seriously not enjoying the Noah's Ark-style weather we've been having on the East Coast lately.
My heroic husband has (hopefully) saved my herbs.
(Those are the old, semi-drowned basil plants; I'm trying to decide whether to leave them be and see whether they'll come back to life or just go ahead and pot some new ones.)