A restrained surface wave resonator with reduced or abated acceleration sensitivity is provided with a stiffening layer, adhesive layers and subsurface horizontal indentations on the substrate to achieve reduced acceleration sensitivity, increased structural rigidity, decreased sensitivity to in-plane deformations, a lightweight device and reduced deleterious effects from environmental shocks and vibration. The substrate of the restrained surface wave resonators features multiple subsurface horizontal indentations in one major substrate surface deposited on a stiffening layer to provide improved structural rigidity against flexure caused by normal acceleration based upon the diminished mass and reduced weight resulting from removal of portions of the substrate subsurface through micro-machining, and it also tends to improve excessive sensitivity to other flexural deformations. The present invention encompasses a restrained surface wave resonator device and a restrained surface wave resonator system.