Hitting shields causes hitlag, as when you hit anything else. Easy way to calculate hitlag (in frames) for most attacks is divide the damage it does by 3, then add 3, and round down. In most cases the opponent also experiences the same amount of hitlag, so you don't need to factor it into shield advantage calculations. Note that hitlag multipliers do not affect shields, so attacks that have these do not create reduced or additional hitlag on the defender.
Attacking shields also pushes you back, although it's barely noticeable without moves that deal high damage like Warlock punch or bowser's fsmash. I'm not sure if you receive pushback while airborne, though.