The growing share of wind and solar power in the total energy mix has caused severe problems in balancing the electrical power production. Consequently, in the future, all fossil fuel-based electricity generation will need to be run on a completely flexible basis. Micro Gas Turbines (mGTs) constitutes a mature technology which can offer such flexibility. Even though their greenhouse gas emissions are already very low, stringent carbon reduction targets will require them to be completely carbon neutral: this constraint implies the adoption of post-combustion Carbon Capture (CC) on these energy systems. Despite this attractive solution, an in-depth study along with a robust optimization of this system has not yet been carried out. Hence, in this paper, a typical mGT with exhaust gas recirculation has been coupled with an amine-based CC plant and simulated using the software Aspen Plus A rigorous rate-based simulation of the CO2 absorption and desorption in the CC unit offers an accurate prediction; however, its time complexity and convergence difficulty are severe limitations for a stochastic optimization. Therefore, a surrogate-based optimization approach has been used, which makes use of a Gaussian Process Regression (GPR) model, trained using the Aspen Plus data, to quickly find operating points of the plant at a very low computational cost. Using the validated surrogate model, a stochastic optimization has been carried out. As a general result, the analyzed power plant proves to be intrinsically very robust, even when the input variables are affected by strong uncertainties.