A microwave printing device comprising an inlet for a filament 1 of an electrically conductive material, an outlet for the filament and a microwave heating device 4 for heating the filament 1 by means of microwave radiation. The microwave heating device 4 comprises at least one coaxial resonator. The coaxial resonator is formed by an outer conductor, which forms a cavity 11, and a coaxial inner conductor. The coaxial resonator also comprises a microwave radiation input for coupling in microwave radiation. The filament 1 preferably forms the inner conductor or part of the inner conductor of the resonator. A system for the additive manufacture of moulds, comprising the microwave printing device, and a process for the additive manufacture of moulds with the aid of the microwave printing device.