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Critically ill new born babies are extremely tiny and vulnerable to external disturbance. Non-invasive health monitoring with body sensor networks is crucial for the survival of these neonates and the quality of their life later on. A key question for health monitoring with body sensor networks is how to obtain reliable electrical power for the sensors, signal amplifiers, filters and transmitters. We propose a wireless power supply based on the principle of inductive contactless energy transfer for use in the neonatal intensive care unit (NICU). The proposed power supply satisfies the requirements of neonatal monitoring and provides continuous power when the neonate is inside the incubator or during Kangaroo mother care. A prototype is designed and built to demonstrate the performance of the power supply and the possibilities for aesthetic features. Experimental results show that the prototype transfers approximately 840 mW of power.