In this paper, a pair of conformal self-resonant spirals, which do not need lumped capacitors to achieve resonance, are designed for wireless powering of biomedical implantable devices. The proposed Conformal Strongly Coupled Magnetic Resonance (CSCMR) wireless powering method uses planar transmitter and receiver configurations that minimize the volume of the system while still providing high power transfer efficiency. Also, self-resonant spirals can be reliably fabricated and are well suited for implantable devices in the human body. The proposed system requires an area of 50 mm×50 mm and achieves a wireless power transfer efficiency of 46.7% at 226 MHz inside the human body for a 30 mm distance from the transmitting element.