Background and objectives: Parameter estimation and uncertainty quantification are crucial in computa-tional cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Many model parameters regarding cardiac electromechanics and cardiovascular hemo-dynamics need to be robustly fitted by starting from a few, possibly non-invasive, noisy observations. Moreover, short execution times and a small amount of computational resources are required for the effective clinical translation. Methods: In the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. Fast simulations and minimal memory requirements are achieved by using an accurate and geometry -specific Artificial Neural Network surrogate model for the cardiac function, matrix-free methods, auto-matic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error. Results: We perform three different in silico test cases, ranging from the ventricular function to the en-tire cardiocirculatory system, involving whole-heart mechanics, arterial and venous hemodynamics. By employing a single central processing unit on a standard laptop, we attain highly accurate estimations for all model parameters in short computational times. Furthermore, we obtain posterior distributions that contain the true values inside the 90% credibility regions. Conclusions: Many model parameters regarding the entire cardiovascular system can be fastly and ro-bustly identified with minimal hardware requirements. This can be achieved when a small amount of non-invasive data is available and when high levels of signal-to-noise ratio are present in the quanti-ties of interest. With these features, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices.