This paper tackles a problem of surface wind speed reconstruction based on synoptic-scale meteorological fields. Specifically, two different approaches are discussed and compared: a pure Machine Learning method, formed by a Support Vector Regression and a genetic algorithm that only considers synoptic pressure as input variable, and a Weather Regimes Classification Technique, based on a k-means clustering of the main three principal components of the geopotential height field and a simple, but efficient, linear regression between the surface pressure gradient and the observed surface wind. Both algorithms are shown to be accurate enough for wind speed reconstruction at medium latitude regions, even when there are only a few years of observations. These methodologies can also be used for filling gaps in wind speed series and, with some modifications and further research, they could be used for wind speed forecasting. The algorithms proposed are fully described and compared in this paper, and their performance has been comparatively evaluated in several real problems of wind speed reconstruction at three sites (Cabauw (The Netherlands), Capel (Wales, UK) and Kaegnes (Denmark)), obtaining excellent results in terms of wind speed reconstruction with moderate complexity in data processing and algorithms.