An asymptotic approach for the standard integral that represents the relative contribution of physical optics scattering of surface waves by a perfect electric conductor plate located vertically over a lossy dielectric half-space is presented. This integral has been obtained in an earlier work by the present authors based on the evaluation of the Electric Field Integral Equation analytically incorporating the set of Green functions by R.W.P. King which apply under High Contrast Approximation. The integral is evaluated using Stationary Phase Method extended for complex phase functions and the accuracy of asymptotic series expansion is tested numerically up to second order. Convergence properties of obtained results are promising to be enrolled in purely analytical-asymptotic investigations of full wave scattering by complex platforms over sea surface and earth.