in star wars for instance, the star destroyers could actually go through asteroid field. But recall the Super class Executor itself was having trouble going in them, the captain saying the shields would severly suffer (but Vader was being an *** so they went in anyway).
If they were allowed in, I expect asteroids to hurt them badly.
(consider SSD Executor a 8km long ship, a rm battleship probably is roughly less than 1km. If we put this proportional to shield power... have a guess.)