In the options, there are boxes where you can set translation, rotation, or scale offesets. depending on which axis you are working in, use a -1 scale in either x, y, or z. Typically if you are working on the right side of the face and want a left side, from front view you will be duplicating at a -1 in X scale. also make sure your original object's pivot point is snapped to grid at the origin.
