Cauchy's technique for interpolating a rational function from samples of frequency responses and/or their derivatives is investigated. This technique can be used to speed up the numerical computations of parameters, including input impedance and RCS of any linear time-invariant electromagnetic system. This technique is utilized to find the far field of a slit conducting cylinder (TM incidence) over a bandwidth utilizing the information about the current and its derivatives at a few sample points. The numerical results are presented are in good agreement with exact computational data. This technique is a true interpolation/extrapolation technique as it provides the same defective result as the original electric field integral equation at a frequency which corresponds to the internal resonance of the closed structure. >