Wrap the sweet potatoes with plastic wrap, and place into the microwave. Cook on High until the sweet potatoes are tender, about 4 minutes, depending on the microwave. Unwrap the potatoes, and refrigerate until cool enough to handle.
Preheat oven to 350 degrees F (175 degrees C). Lightly grease a small baking dish.
Bring the pomegranate juice, water, vinegar, sugar, and cinnamon to a simmer in a small saucepan. Reduce heat to medium-low, and simmer gently for 15 minutes. Meanwhile, peel the potatoes and cut into large cubes; place into the prepared baking dish, and dot with the cubed butter. Pour the pomegranate sauce evenly overtop.
Bake in preheated oven 30 minutes until the pomegranate sauce has thickened into a glaze. Gently stir the potatoes occasionally as they bake to coat them in the glaze.