We show that fast technical fluctuations of microwave signals can be strongly suppressed by cryogenic resonators. The experiments were carried out with sapphire resonators cooled to approximately 6 K at frequencies around 11 GHz. Each sapphire crystal was shaped like a spindle with the rotational and crystal axes aligned within a degree. Noise suppression factors in excess of 50 dB were measured at 10 kHz offset from the carrier. This was achieved by rotating the sapphire spindle and moving the coupling probes relative to its surface. Microwave signals with reduced fast technical fluctuations allow the high-precision tests of fundamental physics, as well as the development of better radars.