An electronic device may include balance-fed antenna structures that do not have direct paths to ground. The antenna structures may serve as a Global Positioning System (GPS) antenna and may have a dipole structure having a first and second antenna resonating element arms. The antenna structures may include a conductive path that conveys antenna signals between a first feed terminal on the first antenna resonating element arm and a transmission line. The conductive path may overlap with the second antenna resonating element arm such that current flow through the conductive path induces corresponding current flow in the second antenna resonating element arm. The antenna structures may include an impedance matching short-circuit stub path that couples the first antenna resonating element arm to the second antenna resonating element arm. Choke inductors may be used to help block indirect paths from the antenna structures to ground through adjacent circuitry.