A sensor device (16a-16d) is provided for monitoring a clamping force (F) exerted by a clamping element (11a-11d) of a clamping device (12a-12d) on a component (14), with at least one strain gauge (30a-30d), which can be arranged on a surface (90, 91) of the clamping element (11a-11d) of the clamping device (12a-12d) and is deformable under the clamping force (F), a transmission module unit (36) based on electromagnetic transmission technology connected to the at least one strain gauge (30a-30d) for detecting a voltage (U5) that is indicative of a deformation (f) of the at least one strain gauge (30a-30d), and an antenna element (38) connected to the transmission module unit (36) for transmitting a signal that is indicative of the detected voltage (U5), and for receiving electromagnetic energy for electrical supply of the transmission module unit (36) and at least one strain gauge (30a-30d).