The energy deposition during the return stroke phase of a pulsed surface discharge is driven by the electrical circuit and the electrical properties of the discharge. To control these factors, a parametric study is performed with varying the circuit parameters, for different discharge lengths and voltages between −19 to −26 kV. The electrical characteristics of the discharge are then simulated using different plasma resistance models, which assume a time-varying resistance: the Toepler model, the Rompe-Weizel model, and the Vlastós model. The model parameters are optimized to fit the experimental results. The analysis shows that for long pulses obtained with large inductance, the three models fare equally well, since the discharge resistance is mainly constant during the pulse. In low-inductance cases, the Toepler model leads to larger errors during the initial current pulse, whereas the Rompe-Weizel and Vlastós models describe with a good agreement the experiments. The discharge resistance evolves during the first 300 ns, then remains mostly constant until the end of the pulse. The constant part of the resistance gives the surface-averaged conductivity of the discharge, which increases linearly with the linear energy dissipated in the discharge. Finally, theoretical estimates of the varying resistance parameters are in fair agreement with the parameters obtained while fitting the experiments, in particular in the Rompe-Weizel case. These findings can be used to estimate the channel resistance of a pulsed surface discharge, and to help optimizing the high-voltage circuit.