A new method is proposed for dominant pole- zero (or pole-residue) analysis of large linear microwave circuits containing both lumped and distributed elements. The method is based on a multipoint Padé approximation. It finds a reduced-order rational s-domain transfer function using a data set obtained by solving the circuit at only a few frequency points. We propose two techniques in order to obtain the coefficients of the transfer function from the data set. The proposed method provides a more efficient computation of both transient and frequency domain responses than conventional simulators and more accurate results than the techniques based on single-point Padé approximation such as asymptotic waveform evaluation.