In this paper, we report a high-precision wireless gap sensor based on a surface acoustic wave (SAW) device. The sensing element is a parallel-plate capacitor whose dimensions are $3{ imes}3;mm^2$, and is attached to the SAW device as an external load. The SAW device, equipped with an RF antenna, serves simultaneously as a signal conditioner and an RF transponder. The center frequency of the SAW device is 450 MHz. The wireless gap sensor prototype exhibits a resolution of 100 nm and a sensing range of $50{mu}m$. The proposed sensor system can be used for remote, high-precision gap measurement in hard-to-reach environments.