According to the certificated private pilot, he rented the airplane in order to refamiliarize himself with flying from the right seat. He invited a certificated flight instructor (CFI), who was also an acquaintance of his, to accompany him on the personal flight. After practicing some emergency landings at the departure airport, the pilots proceeded to a rural area for additional emergency landing practice. The CFI then demonstrated an engine-out approach to an open field, and shortly thereafter she applied power to begin a climb-out; both pilots then heard and felt something strike the airplane. They determined that the airplane was still flyable, and returned to the departure airport where the airplane was landed uneventfully. The CFI stated that during the subject approach, the airplane did not descend any lower than 50 feet above the ground, while the other pilot stated that the airplane did not descend any lower than 100 feet. Neither pilot saw anything that could account for the impact. Inspection of the airplane indicated that the vertical stabilizer incurred substantial damage, most likely due to a wire strike. Efforts to locate the wire were unsuccessful.