Wireless power delivery has the potential to seamlessly power our electrical devices as easily as data is transmitted through the air. However, existing solutions are limited to near contact distances and do not provide the geometric freedom to enable automatic and un-aided charging. We introduce quasistatic cavity resonance (QSCR), which can enable purpose-built structures, such as cabinets, rooms, and warehouses, to generate quasistatic magnetic fields that safely deliver kilowatts of power to mobile receivers contained nearly anywhere within. A theoretical model of a quasistatic cavity resonator is derived, and field distributions along with power transfer efficiency are validated against measured results. An experimental demonstration shows that a 54 m3 QSCR room can deliver power to small coil receivers in nearly any position with 40% to 95% efficiency. Finally, a detailed safety analysis shows that up to 1900 watts can be transmitted to a coil receiver enabling safe and ubiquitous wireless power.