Recently, particular attention has been given to metallic waveguides supporting surface plasmons as promising components for integrated optical devices. However, the use of conventional numerical optimization tools for their design is hindered by the intensive computational effort associated with meshing down to the resolution of the thin metallic layer. In this study, the previous three-point second order accurate finite-difference formula suitable for correctly placing thin dielectric layers within coarse grids is extended to fourth order accuracy by using the generalized Douglas scheme, including the case when thin metallic layers supporting surface plasmons lie wholly between sample points. The improved formulation, combined with an imaginary distance procedure, is used to analyze the eigenmodes of both 2D and 3D thin metal films located upon dielectric substrates. Accurate calculation with coarser meshes than those required by the other standard differencing schemes is demonstrated, thus providing both a significant saving in computational resource and an extra degree of freedom in meshing such structures.