A facility is provided for the wireless resonant charging of rechargeable hearing instruments. The hearing instrument is freely positionable in a charging device for charging purposes. The charging device for the wireless charging has a transmit antenna arrangement, a transmit amplifier for actuating the transmit antenna arrangement and a charging space. The transmit antenna arrangement has two feeding points, which are spatially arranged in relation to the charging space such that a circularly polarized electromagnetic field can thus be generated in the charging space. The transmit amplifier actuates the antennas accordingly to generate a circularly polarized electromagnetic field in the charging space. In the process a coil arrangement generates a circularly polarized HF field. A good resonant coupling, even with a tilted hearing instrument, is possible, in other words with an undetermined and unpredictable orientation and position of the receive coil of the hearing instrument.