Subwavelength cavity resonator microstrip antennas with conjugate left-and right-handed material bilayered substrates are proposed. Details of the antenna design are demonstrated based on the resonant dispersion relation. Due to the phase compensation effects, the total heights of the antennas still keep the subwavelength value, and even achieve further reduction. As is shown, confined bandwidth microstrip antennas with resonant sensitivity are obtained when the solutions to the resonant dispersion relation depend on the frequency. This result makes the considered structures promising candidates as subwavelength cavity resonator microstrip antenna sensors.