I like to charge rude, entitled adults who have no curfew and very few manners double time after their ETA so that they never bother to call me to sit for their poor kids again.

Rude PP: We're leaving now for drinks, dinner and the 10:00 movie.

Me: OK, so you'll be home around 12:30?

Rude PP: I have no idea when we'll come home. I don't have a curfew!

Me: I do need to tell you then that I'll be charging double time after 1 am, and that I will calculate your total owed based on 1/4 hour increments. Have a great night, and stay out as late as you can afford to stay out!

to answer OP's question. I wouldn't insist that I be paid for the unused hour, but I find that most families pay anyway or at least round up. To everyone else "We shouldn't be out too late tonight, maybe 10:30 or 11. Do you have anywhere you need to be afterwards? I'll text if it'll be later."

Our normal babysitter is a family friend who usually stays the night in the guest bedroom. (I did this for her when she was little, and her mom babysat me like that when I was little so it is normal). We usually tell her we'll be home around 1am but "feel free to go to bed before then. We'll turn the hallway light off when we're home so you know we're home". If it is 12:30 (which is usually when she goes to bed) and we know we'll be out later, we'll send a quick text. But since she spends the night, she's more flexible.

When we use another babysitter, we say we'll be home by X time. If we come home earlier, she's paid for the whole time since that is what we booked her for.