In this paper, the SOC of two lead-acid batteries of different ages and capacities of 75 Ah was estimated at the simulation level. The SOC was estimated using the open-circuit voltage method and the Coulomb counter method. Battery models based on an equivalent circuit were used in the simulations, namely the standard GNL model and a new, modified GNL battery model. The paper first describes different battery models and methods for estimating SOC that can be found in the literature. Then, based on experimental measurements, the parameters of resistors and capacitors in the models used were determined, as well as the characteristics of the dependence of SOC on the open-circuit voltage. The model used for the simulations was implemented in the MATLAB-Simulink software package. All components used, their roles and the corresponding parameter values were listed and described. Then, the voltage responses of the battery models used were simulated, which were compared with the experimentally recorded responses, and the SOC responses. The results of SOC estimation using the Coulomb counter method were considered as reference and compared with the results of SOC estimation using the open circuit voltage method. The need for creating a modified GNL model with its associated components was explained, and the values of the integral of the absolute error of voltage and SOC obtained with the considered models were determined and compared, as well as the percentage error of the SOC value obtained based on these models. Finally, a discrete SOC estimator was created, which can be experimentally implemented for real-time SOC estimation.