Dual resonance Rubidium atomic clock requires a microwave resonator tuned to the frequency of the hyperfine transition of the Rubidium 87 isotope. The vapor cell containing the Rubidium atoms is placed within this resonator. In order to achieve a good clock stability, the resonant electromagnetic mode inside the resonant cavity should, in the volume of the vapor cell, have a magnetic field as homogeneous as possible and aligned with an optical field and a constant magnetic field in the vapor cell. Any deviation of this field will excite other atom transitions, and thus deteriorate the clock stability. Moreover, dual resonance clocks are popular in position and telecommunication applications, as for instance Global Navigation Satellite Systems, and should therefore be as lightweight and small as possible. This contribution summarizes the requirements of microwave cavities for dual resonance atomic clocks, and presents some design hints. A typical example is shown to illustrate the feasibility.