This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering, and radiation for structures that include open (dielectric) waveguides, waveguide junctions, as well as launching and/or termination sites and other nonuniformities. Based on the use of a “slow-rise” smooth-windowing technique in conjunction with free-space Green functions and associated integral representations, the proposed approach produces numerical solutions with errors that decrease faster than any negative power of the window size. The proposed methodology bypasses some of the most significant challenges associated with waveguide simulation. In particular, the WGF approach handles spatially infinite dielectric waveguide structures without recourse to absorbing boundary conditions, it facilitates proper treatment of complex geometries, and it seamlessly incorporates the open-waveguide character and associated radiation conditions inherent in the problem under consideration. The overall WGF approach is demonstrated in this paper by means of a variety of numerical results for 2-D open-waveguide termination, launching and junction problems.