1 If you prefer crispy skinned sweet potatoes, you can cook the potatoes in the microwave for 5-6 minutes, then unwrap your sweep potato and transfer it to a baking sheet and bake in an oven preheated to 400 °F (204 °C) for 20 minutes.. Put the plate in the microwave and select a cooking time. Cooking times will vary depending on the size of the potato and the power of the microwave. Most medium to large potatoes will take between 8-12 minutes to cook at full power.