You could try making "mage buster" gear. Enchant your swords and bows with lightning (to drain their magicka) and your armor with magic resistance. You can keep it in your house unless you know you're going up against a mage heavy area.

Alternatively you can brew potions and pound them in combat (I always have two fire resistance potions, two frost resistance potions, etc.) You can also poison your weapons with magicka specific potions (drain magicka, damage regeneration rate, etc.)

When I'm going up against an uber mage I usually sneak attack them with a couple magicka poisoned lightning enchanted bow attacks and then rush them with whirlwind sprint. A couple of power attacks and they're usually crying blood.

Edit: Also remember for those who specialize in the conjuration school, take out the mage and their summoned monster/zombie will collapse into ash. Don't waste your energy on their puppet unless you really have to, they're usually just summon another and another.