Wide-bandgap semiconductors represent an attractive option to meet the increasing demands of micro- and nano-electromechanical systems (MEMS/NEMS) by offering new functionalities, high stability, biocompatibility and the potential for miniaturization and integration. Here, we report on resonant MEMS and NEMS devices with functional layers of SiC, AlN and AlGaN/GaN heterostructures on different substrates, which have been investigated and analysed in the course of an interdisciplinary research focus programme of the German Research Foundation (DFG). The specific deposition and etching technologies necessary for the three-dimensional micro-structuring are explained. Further, the implementation of appropriate electromechanical transduction schemes is discussed. In case of SiC and AlN resonators, actuation and sensing was achieved by a magnetomotive scheme. A piezoelectric coupling scheme where the counter electrode is formed by the two-dimensional electron gas at the interface of the III/V heterostructure was realized for the AlGaN/GaN resonators. Thus, flexural and longitudinal vibration modes were excited and characterized using electrical and optical techniques. The measured key parameters of resonant frequency and quality factor are related to geometry, material and environmental parameters using analytical and finite element (FE) models. Finally, potential sensor applications are experimentally investigated