I like Brightfire's idea. If you don't have a dehydrator, you can always pull just the leaves, wash them, dry them off, then leave them in a dish in the fridge for a couple of weeks - they'll dry to a crisp, perfect for later use. I dry mint this way, sometimes accidentally.
But generally, I'll use celery leaves in, or as a garnish on, chicken soup. Clove, celery, and chicken go so well together.