Electronic-skin (e-skin) sensors can monitor the health of patients remotely in real time. We demonstrate single-crystalline piezoelectric thin-film e-skins that show high-performances that rival sensors made directly on conventional substrates. Excellent crystalline quality of e-skin allows unprecedented demonstration of low-power highly-sensitive wireless strain sensing using surface acoustic wave devices. Also, freestanding membranes of single-crystalline films improve the wearability and sensitivity of sensors.