A simplified methodology is proposed to reduce numerical oscillations in transient responses when transmission lines are represented by a lumped parameter approach employing a π-circuit cascade. These oscillations cause erroneous peaks in electromagnetic transient simulations, which may lead to incorrect interpretations for users. A modified π-circuit cascade, which consists of inserting a damping resistance in series to the capacitor in the traditional π-circuit cascade, is a known topology in the literature, but its influence on transient responses has not been fully studied. In this study, a methodology is shown for selecting an appropriate adjustable factor to reduce the numerical oscillations for a given transmission line of length l without distorting the transient response. The proposed methodology is applied directly in line modelling, facilitating the selection of the damping resistance. The results obtained from the proposed methodology are compared with inverse numerical Laplace transform responses, which is a well-established technique, and with the traditional lumped parameter model, showing an expressive attenuation of the numerical oscillations in the electromagnetic transient responses.