In the linear regime and in the absence of mean flow, the impedance of perforated liners is driven by visco-thermal effects. In this paper, two numerical models are developed for predicting these visco-thermal losses. The first model is the linearized compressible Navier-Stokes equations (LNSE) solved in the frequency domain. The second model is the Helmholtz equation with a visco-thermal boundary condition accounting for the influence of the acoustic boundary layer. These models are compared and validated against measurements. The analysis of the dissipation rate due to viscosity, computed from the LNSE solutions of 4 perforated plates, highlights the presence of edges effects that are not accounted for by any models. It is also shown that a significant portion of the dissipation occurs outside the neck when considering micro perforated plates. The proposed impedance model, based on the Helmholtz equation and a visco-thermal boundary condition, is found to be computationally cheap and accurate.