In a microwavable baking dish, arrange tilapia fillets in a single layer. Dot with pieces of butter, and minced garlic. Sprinkle over fresh tarragon. Cover with waxed paper and microwave on high for 2 minutes.
Turn fillets over, recover, and continue to microwave on high for a further 2 minutes. Remove immediately, sprinkle with apple cider vinegar, and serve.