Abstract: A rigorous Surface Impedance (SI) formulation for planar waveguides is presented. This modal technique splits the modal analysis of the waveguide in two steps. First, we obtain the modes characteristic equations as a function of the SI and, second, we need to obtain the surface impedance values using either analytical or numerical methods. We validate the technique by comparison with well-known analytical cases: the parallel-plate waveguide with losses and the dielectric slab waveguide. Then, we analyze an optical hollow-core waveguide defined by two high-contrast subwavelength gratings validating our results by comparison with reported values. Finally, we show the potential of our formulation with the analysis of a THz hollow-core waveguide defined by two surface-relief subwavelength gratings, including material losses in our formulation.