A transmitter coil inductively couples to a receiver coil contained in a contact lens. In one approach, the transmitter coil is contained in a headgear, for example a head band. When the user wears the headgear, the transmitter coil is positioned on a side of the user's head and between the user's ear and the user's eye opening. In one implementation, a head band loops from one ear behind the user's head to the other ear, and also extends slightly forward of each ear. The transmitter coil(s) may be located in the portion of the headband that extends forward of each ear. This places the transmitter coil close to the receiver coil, typically within 40-50 mm of the user's eye opening, while still maintaining an unobtrusive aesthetic.