The present paper focusses its attention on the application of statistical machine learning techniques and shallow neural network-based models to estimate the wave spectrum in coastal seas. Satellite-borne synthetic aperture radar imagery has been successfully used to estimate the spectrum of oceanic waves. Unfortunately, the analytical methods developed for long oceanic waves could not be adapted for much shorter wind waves dominating coastal seas. Although several deep learning techniques have recently been adapted for the problem, the applicability of lighter and simpler statistical machine learning models and shallow neural networks has not received much attention. This paper explores the applicability of linear regression, polynomial regression, regression trees, and regression forest models alongside their boosted versions and in addition shallow neural network models to estimate the wave spectrum of the Baltic Sea from synthetic aperture radar imagery. The results of the paper clearly demonstrate that boosted models and simple multilayer perceptron are the most accurate, resulting in the lowest mean square error less than 0.5 m and the highest Pearson correlation coefficient reaching 0.8 between the estimated and measured wave spectra, for some frequencies.