Antioxidants are important for maintaining the appropriate balance between oxidizing and reducing species in the body and thus preventing oxidative stress. Many natural compounds are being screened for their possible antioxidant activity. It was found that a mushroom pigment Norbadione A, which is a pulvinic acid derivative, shows an antioxidant activity; the same was found for other pulvinic acid derivatives and structurally related coumarines. Based on the results of in vitro studies performed on these compounds as a part of this study quantitative structure–activity relationship (QSAR) predictive models were constructed using multiple linear regression, counter-propagation artificial neural networks and support vector regression (SVR). The models have been developed in accordance with current QSAR guidelines, including the assessment of the models applicability domains. A new approach for the graphical evaluation of the applicability domain for SVR models is suggested. The developed models show sufficient predictive abilities for the screening of virtual libraries for new potential antioxidants.