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The assessment of environmental policies and sustainability in socio-ecological systems (SES) should be tackled from a holistic perspective, using methodologies such as dynamic system models. However, the integral assessment of SES generally suffers from high levels of uncertainty. In this work, the potential of sensitivity analysis (SA) to assess uncertainty and its implications in SES models, specifically in the Fuerteventura sustainability model, has been explored. An extensive SA was applied in different stages of model development and application. The different SA techniques applied allowed, besides a detailed assessment of robustness, the identification of leverage points and their application to define environmental policies and management measures intended to improve sustainability. The results suggest that measures based on leverage points identified by the SA in the model are more effective than others proposed so far by different agents. Furthermore, the assessment of uncertainty of measures thought to contribute to sustainability shows that, when uncertainty ranges are considered, the thresholds of some sustainability indicators might be exceeded, whereas mean values would not. Therefore, the surpassing of some sustainability thresholds might go unnoticed if uncertainties are not considered in the policy analysis. This work shows SA to be a powerful tool that provides important insights to policy makers and end users, with regard to improving environmental policies for sustainability.