Instead of waiting last minute, you'd think a large company would have planning to renew certificates X amount of time before they expire. Alas I understand it's not that simple.
There's a remarkable number of ways for this simple thing to go wrong. To prevent a future repeat, we got rid of our calendar reminders (which we started ignoring once we both thought the change had been made) and wrote a script that emailed us based on the time to expiration of the live cert. This is a much better method.
Of course, give us enough years and I'm sure we'll manage to find a way to get this new setup wrong.
Thanks for the reminder.