Micromechanical structures having at least one lateral capacitive transducer gap filled with a dielectric and method of making same are provided. VHF and UHF MEMS-based vibrating micromechanical resonators filled with new solid dielectric capacitive transducer gaps to replace previously used air gaps have been demonstrated at 160 MHz, with Q's.about.20,200 on par with those of air-gap resonators, and motional resistances (R.sub.x's) more than 8.times. smaller at similar frequencies and bias conditions. This degree of motional resistance reduction comes about via not only the higher dielectric constant provided by a solid-filled electrode-to-resonator gap, but also by the ability to achieve smaller solid gaps than air gaps. These advantages with the right dielectric material may now allow capacitively-transduced resonators to match to the 50-377.OMEGA. impedances expected by off-chip components (e.g., antennas) in many wireless applications without the need for high voltages.