Microwave photonic technologies, which upshift the carrier into the optical domain, have facilitated the generation and processing of ultra-wideband electronic signals at vastly reduced fractional bandwidths. For microwave photonic applications such as radars, optical communications and low-noise microwave generation, optical frequency combs are useful building blocks. By virtue of soliton microcombs, frequency combs can now be built using CMOS-compatible photonic integrated circuits. Yet, currently developed integrated soliton microcombs all operate with repetition rates significantly beyond those that conventional electronics can detect, preventing their use in microwave photonics. Access to this regime is challenging due to the required ultra-low waveguide loss and large dimensions of the nanophotonic resonators. Here, we demonstrate soliton microcombs operating in two widely employed microwave bands, the X-band (similar to 10 GHz, for radar) and the K-band (similar to 20 GHz, for 5G). Driven by a low-noise fibre laser, these devices produce more than 300 frequency lines within the 3 dB bandwidth, and generate microwave signals featuring phase noise levels comparable to modern electronic microwave oscillators. Our results establish integrated microcombs as viable low-noise microwave generators. Furthermore, the low soliton repetition rates are critical for future dense wavelength-division multiplexing channel generation schemes and could significantly reduce the system complexity of soliton-based integrated frequency synthesizers and atomic clocks.