We report our studies on using microwave-optical double-resonance (DR) spectroscopy for a high-performance Rb vapour-cell atomic clock in view of future industrial applications. The clock physics package is very compact with a total volume of only 0.8 dm3. It contains a recently in-house developed magnetron-type cavity and a Rb vapour cell. A homed-made frequency-stabilized laser system with an integrated acousto-optical-modulator (AOM) – for switching and controlling the light output power– is used as an optical source in a laser head (LH). The LH has the overall volume of 2.5 dm3 including the laser diode, optical elements, AOM and electronics. In our Rb atomic clock two schemes of continuous-wave DR and Ramsey-DR schemes are used, where the latter one strongly reduces the light-shift effect by separation of the interaction of light and microwave. Applications of the DR clock approach to more radically miniaturized atomic clocks are discussed.