In this article, an investigation of a free-piston Stirling engine-based micro-cogeneration (μCHP) unit is presented. This work is a step towards making the system calculations more reliable, based on a data-driven model, which enables the time-domain simulation of the μCHP behavior. A laboratory setup was developed that allowed for the measurement of a micro-cogeneration unit during long-term operation with a variable thermal load. The maximum efficiency of electricity generation was equal to 13.2% and the highest overall efficiency was equal to 95.7%. A model of the analyzed μCHP system was developed and validated. The simulation model was based on the device’s characteristics that were obtained from the measurements; it enables time-domain calculations, taking into account the different operating modes of the device. The validation of the system showed satisfactory compliance of the model with the measurements: for the period modeled of 24 h, the error in the heat generation fluctuated in the range 0.31−4.50%, the error in the electricity generation was in the range 2.48−4.70%, the error in the natural gas consumption was in the range 0.26−4.59%, and the engine’s runtime error was in the range 0.14−8.58%. The modelling process is easily applicable to other energy systems for detailed analysis.