It seems to me that some posts are too harsh with the OP: *A rules require that UA provides hotel+food vouchers for controllable delays for legal connections, no matter how close to the MCT these are.
Regarding compensation, unfortunately a few k miles or a small certificate is the standard... a delay is very different from denied boarding.
In a delayed arrival situation I always assume they will close the door at T-10 and aim at making to the gate at T-15 by sprinting if necessary. In a couple of occasions, I have seen planes held a few minutes waiting for passengers, but I think it might be more for other operational reasons and in those cases they keep the door open...