A strain gauge with a strain-sensitive electrical resistor track and connector electrodes for contacting the resistor track arranged on a carrier substrate is provided with a protective coating having inorganic materials and covering at least part of the carrier substrate and/or of the resistor track and/or of the connector electrodes. The build-up structure of the protective coating over the range of the coating thickness is inhomogeneous, and the protective coating is underlaid with a surface-smoothing polymer layer which evens out rough surface portions of the area to be coated. The layer thickness of the surface-smoothing layer is at least equal to the thickness of the protective coating. A strain gauge of this type can be used in a force-measuring cell, where the surface-smoothing layer and the protective coating can be deposited after an uncoated strain gauge has been installed on the deformable body of the force-measuring cell.