We have developed a method to calculate the distribution of fundamental and spurious fields in a metallic cylindrical cavity with superconducting endplates in which signals at two different frequencies are injected. The nonlinearity in the superconductor produces the typical intermodulation effects if the frequencies of the injected signals are sufficiently close to each other and near a resonant mode. Our method uses harmonic balance to match the fields in the cavity with the currents on the endplates. The method can be used for a variety of nonlinear models of the superconducting endplate, and could be the base for a nondestructive procedure to extract the nonlinear parameters of an HTS sample from RF measurements. Our analysis is restricted to the TE011 mode, but the method can be applied to any propagating mode in the cylindrical cavity. Closed-form equations for the case of square-law nonlinearities in the superconductor are derived and used to check the validity of the harmonic balance calculation.