A method is developed for the extraction of the orientation and geometry of an electromagnetic scatterer from its pulse response in the time domain. The scheme considered employs a narrow interrogating video pulse with a large bandwidth, with the target backscatter response obtained over a finite number of interrogating directions. The inverse scattering algorithm uses the first five moment condition integrals of time-domain electromagnetic theory to recover the Rayleigh coefficient and the next higher order nonzero coefficient of the power series expansion in the wave number from the object backscattering response. Numerical estimates of the dimensions and orientation of an assumed elliptical scatterer are then obtained from the coefficients thus recovered. Numerical simulations have demonstrated the accuracy of the Coefficient Recovery Technique (CRT) and the geometry recovery scheme for a conducting scatterer, and the satisfactory performance of the CRT under noisy conditions.