An inductive wireless power transfer system is proposed as a power supply for an on-line monitoring system for an overhead catenary. Because of the high voltage (25 kVrms) applied to the catenary, galvanic isolation was required to supply power to the attached monitoring system. The proposed wireless power system was able to transmit 50 W over a distance of 60 cm at 6.78 MHz. Design methodologies for the transmitter and the receiver coils, 6.78-MHz GaN-based full-bridge inverter, and rectifier are proposed in this paper. Pareto optimality, a multi-objective optimization technique, was used to determine optimal solutions in terms of efficiency and copper usage. A 100-W, 6.78-MHz full-bridge inverter was developed using 100 V, 35 A, E-HEMT GaN MOSFETs. Because of the high operating frequency, two factors were considered in the design of the full-bridge inverter, (1) close placement of the gate driver and the switch to minimize parasitic inductance and the resulting fluctuation of the drive signal and (2) effective heat dissipation from the switches and gate drivers for a high power rating. In addition, a full-wave rectifier was built using Schottky barrier diodes with a reverse recovery time of a few tens of nano-seconds. The developed wireless power system was experimentally evaluated. The measured coil-to-coil efficiency was 77%, and the measured efficiencies of the inverter and the rectifier were 92% and 93%, respectively. The overall system efficiency was 57% for a transfer of 47 W. Finally, the dependences of the efficiency on the distance, operating frequency, and load were evaluated.