This paper presents a general methodology based on the matrix pencil method (MPM) for the fitting of frequency-domain responses in order to be properly represented in time-domain analysis. By virtue of the proposed method, a rational fitting of the frequency-domain responses can be inferred, which, in turn, helps with their inclusion into time-domain calculations. The proposed technique is well suited for the estimation of any type of function including the case of those with superimposed noise. The main feature of the method is its direct solution, hence avoiding any iteration in the estimation process. Moreover, the method does not require starting poles as opposed to the vector-fitting (VF) method. This paper presents the validation of the proposed approach by fitting the frequency responses of general a priori known functions, artificially created noisy functions and those of power components, namely: the elements of a power transformer admittance matrix and the characteristic admittance and propagation functions of a single-core sheathed cable. Finally, a time-domain analysis referring to lightning transients on a transmission line is presented.