Cogeneration systems with microturbine allow recuperating the low-quality energy that is normally wasted in conventional power generation systems. The aim of this article is to evaluate a cogeneration system using a Capstone 30-kW gas microturbine, to estimate the second law efficiency by training a backpropagation neural network using a thermodynamic model developed in HYSYS®, and to assess the performance indicators using Matlab®. The results show that the highest exergy destruction rate is in the combustion chamber, followed by the compressor and the heat recovery stage in the steam generator. From the parametric analysis it can be inferred that increasing the compression ratio, the isentropic compressor efficiency and the isentropic expander efficiency of the gas microturbine improves the overall thermodynamic system performance. In addition, the outlet temperature of the preheater significantly affects the thermal and exergoeconomic system performance. However, only parameters that present good performance and can be improved for prediction purposes were considered in neural network training.