For modern electrical rail systems, the pantograph-catenary dynamic performance is one of the most critical challenges. Too much fluctuation in contact forces leads to either accelerated wear of the contacting components or losses of contact and, consequently, arcing. In this work, inertance-integrated pantograph damping systems are investigated with the objective of reducing the contact force standard deviation. Firstly, a multibody pantograph model is developed with its accuracy compared with experimental data. The model is improved through the calibration of the pantograph head suspension parameters and the introduction of both non-ideal joint and flexibility effects. Using the calibrated model, beneficial inertance-integrated damping systems are identified for the pantograph suspension. The results show that the configuration with one inerter provides the best performance among other candidate layouts and contends a 40% reduction of the maximum standard deviation of the contact force over the whole operating speed range in the numerical modelling scenario analysed. Considering the identified configuration, time-domain analysis and modal analysis are investigated. It has been shown that the achieved improvement is due to the fact that with the beneficial inertance-integrated damping system, the first resonance frequency of the pantograph system coincides with the natural frequency of the catenary system.