Use skill dice which are a different color than your attribute dice.
You get +1 damage or some other game effect for each skill die that is higher than any attribute die.
example: you are rolling 6d+0 with 3 skill dice(s) and 3 attribute dice(a). If the roll is (6s, 5s, 4a, 3s, 3a, 1a), then you have two skill dice that are higher than any attribute dice, for a +2 effect.
You could also have certain other options which could be player-specified when they make an attack. For instance, you might have a set of options:
a) each high skill die is +1 damage before armor
b) each high skill die gives +1 on your next attack
c) each high skill die is +2 on your next defense
And a player could say what option they wanted before they attacked, based on the combat situation. Do they want a stronger hit, a more likely followup or a better defense?