Agent-based models can display very complex behaviour such as tipping points and adaptation, following from nonlinear feedbacks between agents and their environment. This complex behaviour is of pivotal interest to modellers and analysts. Sensitivity analysis is an indispensable tool for the analysis of models, but current methodologies are not particularly well-suited for the analysis of agent-based models for two reasons: 1/ agent-based models are too complex to be analysed using standard methodologies that exist for the analysis of linear models or models of ordinary differential equations, and 2/ statistics commonly used in sensitivity analysis are significantly obscured when tipping points and strong nonlinearities are present. The goal here is to develop methods for sensitivity analysis that can also be utilized to analyse agent-based models. To test their performance and verify the results two test cases are used that are based on models of ordinary differential equations which contain tipping points and strong nonlinearities but still are simple enough to allow for the use of traditional methods.