Equivalent circuits based on the telegrapher's equations are suited for calculation of transient phenomena in transmission lines in the time domain. In order to simulate the frequency dependent properties of real lines, one-port networks are included in the equivalent circuit of each section. These proposed equivalent circuits give the possibility to calculate transients in transmission lines in the time domain, using responses of line parameters modified for high frequencies. Different approaches for the determination of the lines one-port network equivalent parameters simulating this frequency dependence of per unit length line parameters are considered. The results of such an approach for the analysis of fast processes in systems with small losses are affected by oscillations caused by the imperfections of the mathematical model of the line. An approach permitting to damp these oscillations and to increase the accuracy and efficiency of the transient calculations is proposed and justified. The method is based on an artificial increase of losses in the line in a range of frequencies not essential for a valid reproduction of the transient process