We present our microwave spectroscopic studies on laser-microwave double-resonance (DR) signals obtained from a micro-fabricated Rb vapor cell. This study focuses on the characteristics and systematic shifts of the ground-state 'clock transition' in Rb-87 (vertical bar F-g = 1, m(F) = 0 > -> vertical bar F-g = 2, m(F) = 0 >) used in Rb atomic clocks, and represents a first step toward a miniature atomic clock based on the DR scheme. A short-term clock instability below 2x10(11)tau(-1/2) is demonstrated, staying below 10(-11) up to tau = 10(4) s.