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In robotics, precise models are critical for ensuring safety and functionality. However, acquiring a precise model characterizing a system’s dynamics can be challenging. One of the alternatives to address this issue is system Identification, which aims to obtain models through physical and experimental observations. In this manner, the developments in machine learning algorithms, such as neural networks, have significantly improved the modeling of complex and nonlinear phenomena. In this work, a mass-spring-damper (MSD) system and a low-cost original elastomer-based Series Elastic Actuators (eSEA) assembly are used to evaluate the performance of system Identification models. The black-box models selected are variations of the AutoRegressive Moving Average with eXogenous input (ARMAX) algorithm. The gray-box model aims to estimate the parameters of 4 friction models; the optimization is done utilizing physics-informed neural networks (PINNs). For both case studies, the PINNs outperformed the black-box models. In the didactic example, the parameters obtained are close to the ground truth, and the highest determinant coefficient obtained is 0.99. The friction model that best represents the robotic actuator is the LuGre model, with the parameters obtained using the PINNs, outperforming the best black-box model by lowering the mean absolute error (MAE) by 30.83%. With a determinant coefficient of 0.94, the model shows a high capacity for describing the multiple nonlinearities present in the system.