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Nowadays there is an increasing need for radically miniaturized and low-power atomic frequency standards, for use in mobile and battery-powered applications. For the miniaturization of double-resonance (DR) Rubidium (Rb-87) atomic clocks, the size reduction of the microwave cavity or resonator (MWR) to well below the wavelength of the atomic transition (6.835 GHz for Rb-87) has been a long-standing issue. Here we present a newly developed miniaturized MWR, the mu-LGR, consisting of a loop-gap resonator based cavity with very compact dimensions (volume < 0.9 cm(3)). The mu-LGR meets the requirements of the atomic clock application and its assembly can be performed using repeatable and low-cost techniques. The concept of the proposed device was validated through simulations and prototypes were successfully manufactured and tested. High-quality DR spectra and first clock stabilities were demonstrated experimentally, proving that the mu-LGR is suitable for integration in a miniaturized atomic clock.