A microelectromechanical (MEM) resonator is disclosed which has a linear or ring-shaped acoustic resonator suspended above a substrate by an acoustic reflector. The acoustic resonator can be formed with a piezoelectric material (e.g. aluminum nitride, zinc oxide or PZT), or using an electrostatically-actuated material. The acoustic reflector (also termed an acoustic mirror) uses alternating sections of a relatively low acoustic impedance Z.sub.L material and a relatively high acoustic impedance Z.sub.H material to isolate the acoustic resonator from the substrate. The MEM resonator, which can be formed on a silicon substrate with conventional CMOS circuitry, has applications for forming oscillators, rf filters, and acoustic sensors.