An approximate but sufficiently accurate high frequency solution is developed in this paper for analyzing the problem of electromagnetic plane wave scattering by an open-ended, perfectly-conducting, semi-infinite parallel-plate waveguide with a thin layer of lossy or absorbing material on its inner wall, and with a planar termination inside. The high frequency solution combines uniform geometrical theory of diffraction (UTD) and aperture integration (AI) methods. The present method has several advantages in comparison with other methods.