The present subject matter provides technical solutions for the technical problems facing cryogenic ion traps by providing a cryogenic radio-frequency (RF) resonator that is compact, monolithic, modular, and impedance-matched to a cryogenic ion trap. The cryogenic RF resonator described herein is power-efficient, properly impedance-matched to the RF source, has a stable gain profile, and is compatible with a low temperature and ultra-high vacuum environment. In some examples, the gain profile is selected so that the cryogenic RF resonator acts as a cryogenic RF amplifier. This cryogenic RF resonator improves the performance of ion traps by reducing or minimizing the heat load and reducing or minimizing the unwanted noise that may erroneously drive trapped ions. These features of the present subject matter improve the performance of atomic clocks and mass spectrometers, and especially improve the performance of trapped ion quantum computers.