One of the main challenges associated with utilisation of the renewable energy is the need for energy storage to handle its intermittent nature. Power-to-Gas (PtG) represents a promising option to foster the conversion of renewable electricity into energy carriers that may attend electrical, thermal, or mechanical needs on-demand. This work aimed to incorporate a stochastic approach (Artificial Neural Network combined with Monte Carlo simulations) into the thermodynamic and economic analysis of the PtG process hybridized with an oxy-fuel boiler (modelled in Aspen Plus®). Such approach generated probability density curves for the key techno-economic performance indicators of the PtG process. Results showed that the mean utilisation of electricity from RES, accounting for the chemical energy in SNG and heat from methanators, reached 62.6%. Besides, the probability that the discounted cash flow is positive was estimated to be only 13.4%, under the set of conditions considered in the work. This work also showed that in order to make the mean net present value positive, subsidies of 68 €/MWelh are required (with respect to the electricity consumed by PtG process from RES). This figure is similar to the financial aids received by other technologies in the current economic environment.