The possibility of increasing the sensitivity of magnetoimpedance (metal) magnetic field sensors by including a high-frequency resonant circuit is considered. Various schemes of resonant circuits are presented, allowing one to increase the sensitivity of a metal magnetoimpedance sensor at a frequency of 75 MHz. The best results were obtained for a Q multiplication circuit that increases the transmission coefficient of the sensor from the external magnetic field strength from 31 to 132%/Oe with a narrowing of the bandwidth to 2.5 MHz, which results in an increase of the signal-to-noise ratio by an order of magnitude. This approach using quadrature demodulation of the signal makes it possible to distinguish signals of an alternating magnetic field with an amplitude of 1 nT with a signal-to-noise ratio of 10 dB. The proposed method can be applied for magnetoimpedance and magnetoresistive magnetic field sensors as well as for metal strain gauges during highly sensitive measurements.