A method of forming a micromechanical resonator includes forming a resonator body anchored to a substrate by at least a first anchor. This resonator body may include a semiconductor or other first material having a negative temperature coefficient of elasticity (TCE). A two-dimensional array of spaced-apart trenches are provided in the resonator body. These trenches may be filled with an electrically insulating or other second material having a positive TCE. The array of trenches may extend uniformly across the resonator body, including regions in the body that have relatively high and low mechanical stress during resonance. This two-dimensional array (or network) of trenches can be modeled as a network of mass-spring systems with springs in parallel and/or in series with respect to a direction of a traveling acoustic wave within the resonator body during resonance.