The diffraction by a slit formed by two semi-infinite parallel-plate waveguides is rigorously analyzed using the WienerÀHopf technique for the H-polarized plane-wave incidence. Introducing the Fourier transform for the scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous WienerÀHopf equations, which are solved via the factorization and decomposition procedure leading to exact and highfrequency asymptotic solutions. Taking the inverse Fourier transform and applying the saddle point method, the scattered field in real space is derived. Numerical examples of the far-field intensity are presented and scattering characteristics of the slit are discussed.