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I've never used antimagic. How would I know which unit it will target? Usually, I managed to overwhelm enemies with spells without using antimagic.
However, lightning, blessing, blinding, and chain lightning are indispensable. If all else fails, you send a hero with a decent spellpower and a squad of dragons to meet the enemy. You can confuse them with Armageddon or a storm of elements, and then engage in combat.