A very high-Q, low insertion loss resonator can be achieved by storing many overtone cycles of a lateral acoustic wave (i.e., Lamb wave) in a lithographically defined suspended membrane comprising a low damping resonator material, such as silicon carbide. The high-Q resonator can sets up a Fabry-Perot cavity in a low-damping resonator material using high-reflectivity acoustic end mirrors, which can comprise phononic crystals. The lateral overtone acoustic wave resonator can be electrically transduced by piezoelectric couplers. The resonator Q can be increased without increasing the impedance or insertion loss by storing many cycles or wavelengths in the high-Q resonator material, with much lower damping than the piezoelectric transducer material.