The paper presents the analysis of the discontinuity between a coaxial and a generalized stripline waveguide and its application to the characterization of a probe inside a rectangular waveguide. The probe is modeled by a stripline whose inner conductor is stepped. For thin probes, just a reduced number of sections is needed and its characterization can be obtained very efficiently. The mode-matching technique is employed for analyzing the basic discontinuity, and the inner cross products between the modes are computed by means of the Bessel-Fourier series, reducing the computation time with respect to a pure numerical integration. The simulation results are compared with those obtained by other numerical techniques.