A novel and fast hybrid Finite Element Method/Method of Moments (FEM/MoM) technique in conjunction with Asymptotic Waveform Evaluation (AWE) is presented to calculate radar cross section (RCS) over a wide frequency range of a cavity-backed aperture in an infinite ground plane. The hybrid FEM/ MoM technique when applied to the cavity-backed aperture results in an integro-differential equation with electric field as the unknown variable. The electric field obtained from the solution of the integro-differential equation is expanded as a function of frequency in Taylor series. The coefficients of the Taylor series are determined using the frequency derivatives of this equation. The Taylor series is then matched via the Pad'e approximation to obtain a rational polynomial representation for the electric field, which can be used to extrapolate the electric field over a frequency range. The RCS of the cavity-backed aperture is calculated using the electric field at different frequencies. Numerical results for a square cavity, a circular cavity, and a cavity-backed microstrip patch are presented over a frequency range. Good agreement between AWE and the exact solution over the frequency range is obtained and the present method proved to be cost effective in terms of CPU time compared to calculating RCS at each frequency.