Or have one of those pager systems some restaurants use to let you know your burger is ready. You don't need one for every attendee; just the ones who are parents, doctors, etc., and specifically come up to request one (and register it in their name).
Pagers solve the issue for such professions, firefighters have them, those things are loud... For parents? Perhaps, but if you're paying for daycare you might as well trust them to get things right.
Also, not a daycare center, but a babysitter. For many of the babysitters we get, we're meeting them for the first time when they show up at our door; that's just reality these days. And it's not uncommon for them to text us while we're out, though thankfully no emergencies so far.
