The formulas for the boundary diffraction of electromagnetic waves are derived by using the Luneburg diffraction formulas and Cauchy's integral formula under the condition that the boundary values are represented by harmonic functions. In the special case that the incident electromagnetic waves are diffracted from a circular aperture, Poisson's formula is used to obtain another form of the boundary diffraction formulas. When the boundary values are the solutions of the Dirichlet problem in two dimensions, formally represented boundary diffraction formulas for electromagnetic waves are obtained. The boundary diffraction of partially coherent waves is also analyzed.