We investigate the interface of a glass-forming fluid. When we apply shear flow along the interface, we find that the surface tension changes with the shear rate. An important point is that the standard method of determining surface tension from the pressure anisotropy across the interface can be misleading in a non-Newtonian fluid. It can result in an effective surface tension that combines contributions from both the bulk fluid and the interface. We therefore use the pressure anisotropy to distinguish between the bulk and interfacial regions. This allows us to separate the different contributions and determine a genuine shear-rate-dependent surface tension. These findings are relevant for experimental and computational techniques used to characterize the interfacial rheology of complex fluids.