The highest beam efficiency in a wireless power transfer (WPT) system that uses focusing components was 51%. Achieved by William Brown in 1964, it used a ~3 m diameter reflector for a transfer distance of 7.62 m. This record was unbeaten for 58 years until now, as we present a system that surpasses Brown's work by 25%. Using the quasioptical framework for reducing spillover losses in WPT, we present a double-reflector system that achieved a higher beam efficiency than the state-of-the-art, when taking into account the system components. The transmitting and receiving antennas were 3D-printed conical smooth-walled horn antennas, specially designed for this system. The theoretical analysis enabled the design of a five-meter system, whose energy focus location has been experimentally verified. Following this successful measurement, the complete system was experimented upon, whose results are here described, enabling a high beam transfer efficiency of 63.75%, validating the theoretical results obtained previously. Additionally, the advantage of using quasioptics in radiative wireless power transfer applications is discussed, as well as the sensitivity of its systems by analyzing how the efficiency changes with variations of different parameters. Finally, a comparison of this system with the state-of-the-art is done by the proposal of new figures-of-merit, relating the systems' physical dimensions and beam efficiency. Through them, it becomes clear that our system outperforms the previous works in terms of the beam efficiency achieved when taking into account the system components used. Furthermore, this research is a paradigm shift by presenting a promising path for future WPT research through quasioptics, one that may lead to developments of such high efficiencies that will potentially enable commercial application of this technology in solving power supply issues in our society.