A wireless power system capable of transmitting power through the skin over distances ranging from a few inches to several feet includes an external transmitting coil assembly and a receiving coil assembly. A transmitting resonant coil and a receiving resonant coil are constructed as to have closely matched or identical resonant frequencies so that the magnetic field produced by the transmitting resonant coil is able to cause the receiving resonant coil to resonate strongly also, even when the distance between the two resonant coils greatly exceeds the largest dimension of either coil. The receiving resonant coil then creates its own local time varying magnetic field, which inductively produces a voltage to provide power to an active implantable medical device or implantable rechargeable battery.