A method for numerically extracting the diffraction and surface wave scattering mechanisms present in the coated edge is described. An exact boundary integral formulation is used without resorting to the impedance boundary condition approximation. To handle the semi-infinite problem numerically, the non-decaying physical optics (PO) and surface wave fields are removed from the boundary integral equation such that the final discretization domain involves only a finite region near the edge. Numerical diffraction coefficients and surface wave launch coefficients are extracted from the scattered field. Solutions to several finite sized coated strips are constructed using the numerical diffraction coefficients and are shown to be valid for a variety of strip configurations.