Coupled human-natural systems are complex systems composed of interacting human and natural components. Managing these systems requires careful characterization of which system uncertainties drive their dynamics and how human actions interact with the natural system to create feedbacks. This dissertation advances exploratory modeling techniques to discover interactions and dependencies between elements of the human and natural systems to better characterize risks to each component. These techniques are illustrated on two socio-ecological systems serving multiple objectives: a managed lake and a multi-reservoir system. These case studies illustrate ways in which the coupled dynamics in these systems can differ under alternative human control strategies due to complex interactions between the two components, and their conclusions have important implications for managing several common challenges in socio-ecological systems, namely: tipping points, problem formulation uncertainty and risk characterization. The first case study on managed lakes shows that state-dependent control rules describing a town's pollutant discharge policy are more robust to deep uncertainties in lake model parameters than static, temporal control rules, reducing the probability of the lake's water quality crossing an irreversible tipping point. Furthermore, adaptive state-dependent control rules can be readily coupled with statistical learning techniques to better navigate deeply uncertain lake parameterizations. The second case study illustrates how uncertainty in how to formulate a socio-ecological management problem, specifically a multi-objective, multi-reservoir operating problem, strongly influences the resulting human control strategies found to be optimal, and consequently how those strategies impact the system dynamics. This underlines the importance of exploring rival framings of how to formulate socio-ecological management problems to discover unintended consequences of different formulations. Finally, further work on the same multi-reservoir problem analyzing the impacts of plausible changes in monsoonal dynamics and sectoral water demands highlights the importance of sampling a broad range of potential drivers of change to characterize the most important risks to coupled human-natural systems, as failure modes may result from mixtures of complex factors. In summary, this work advances exploratory modeling techniques to yield a greater understanding of the dynamics of coupled human-natural systems that can be used to inform adaptive management strategies for building more robust and resilient systems.