A wireless power receiving system for a mobile electronic device that includes a high-Q repeater resonator comprising at least an inductor and a capacitor and having a Q-factor Q1. The inductor of the repeater resonator is enclosed in a removable sleeve of the mobile electronic. The system also includes a high-Q device resonator comprising at least an inductor and a capacitor and having a Q-factor Q2. The device resonator is integrated in the mobile device and electrically connected to the mobile electronic device, and the square root of the product Q1 and Q2 is greater than 100.