A simulation study to assess the potentiality of sea surface wind vector estimation based on the approximation of the forward model through Neural Networks and on the Bayesian theory of parameter estimation is presented. A polarimetric microwave radiometer has been considered and its observations have been simulated by means of the two scale model. To perform the simulations, the atmospheric and surface parameters have been derived from ECMWF analysis fields. To retrieve wind speed, Minimum Variance (MV) and Maximum Posterior Probability (MAP) criteria have been used while, for wind direction, a Maximum Likelihood (ML) criterion has been exploited. To minimize the cost function of MAP and ML, conventional Gradient Descent method, as well as Simulated Annealing optimization technique, have been employed. Results have shown that the standard deviation of the wind speed retrieval error is approximately 1.1 m/s for the best estimator. As for the wind direction, the standard deviation of the estimation error is less than 13° for wind speeds larger than 6 m/s. For lower wind velocities, the wind direction signal is too weak to ensure reliable retrievals. A method to deal with the non-uniqueness of the wind direction solution has been also developed. A test on a case study has yielded encouraging results.