High efficiency resonator coils for large gap resonant wireless power transfer (WPT), and a coil design methodology are disclosed. Resonator coils comprise a coil topology defined by coil parameters in which turn dimensions, such as trace widths and spacings of each turn, are configured to reduce or minimize a variance of the z component of magnetic field, over an area of a charging plane at a specified distance, or distance range, from the coil. A Tx resonator coil comprises a capacitor arrangement of tuning and network-matching capacitors for improved coil-to-coil efficiency and end-to-end WPT system performance, e.g. for applications such as through-wall WPT, in the range of tens of watts to at least hundreds of watts. Planar resonator coil topologies are compatible with fabrication using low cost PCB technology, e.g. with multi-layer metal, to reduce losses and improve thermal performance.