One thing I do, and this requires a certain level of trust, is have my players pre-roll while they are waiting for their turn.
So, they pre-roll the to-hit and find out which AC they hit. Then they roll the damage for that hit. Repeat for multiple attacks. When it is their turn they'll say "Does AC 28 hit?" "Yes." "Okay, damage is 34" etc etc
Now, the pre-planning may not work because of actions that happen before the players turn but usually the pre-rolling is quite helpful. Or if you have players that fudge their dice rolls, but that is a whole other problem.