I was on a trip with a 4 year old, and I had underestimated how much they could walk and how quickly. We were running late for our ADR at Sci Fi by about 15 min. I remember calling ahead to the restaurant (about 30 min) to let them know I was running late by 15 min. They had said no problem.
Like others have said already, if you know it's tight, you might want to just shift your plans a bit. That said, life happens, and if you find yourself in that position, I think the best you can do at that point is to let the restaurant know as far ahead as possible as a courtesy.