Analysis of discontinuity in waveguide plays an extremely crucial role in the design of resonators and filters. Equivalent network of a coaxial line terminated in a circular waveguide is introduced first, and then Rayleigh-Ritz Variational Method is adopted to obtain the upper and lower bounds of the discontinuity capacitance. Numerical results of Rayleigh-Ritz Variational Method agree very well with simulation results of HFSS and results in the reference. The example of the variational computation shows that if arithmetical mean of the upper and lower bounds of the capacitance is taken as the value of the equivalent capacitance, then of majority frequencies raging from low frequency to near cutoff for the lowest evanescent mode of the structure, the percentage errors between the values of discontinuity capacitance computed from variational technique and HFSS simulation ones gained by FEM, are lower than 1％.