Many countries are currently dealing with the COVID-19 epidemic and are searching for an exit strategy such that life in society can return to normal . To support this search, computational models are used to predict the spread of the virus and to assess the efficacy of policy measures before actual implementation . The model output has to be interpreted carefully though, as computational models are subject to uncertainties . These can stem from, e.g., limited knowledge about input parameters values or from the intrinsic stochastic nature of some computational models . They lead to uncertainties in the model predictions, raising the question what distribution of values the model produces for key indicators of the severity of the epidemic . Here we show how to tackle this question using techniques for uncertainty quantification and sensitivity analysis . We assess the uncertainties and sensitivities of four exit strategies implemented in an agent-based transmission model with geographical stratification . The exit strategies are termed Flattening the Curve, Contact Tracing, Intermittent Lockdown and Phased Opening . We consider two key indicators of the ability of exit strategies to avoid catastrophic health care overload: the maximum number of prevalent cases in intensive care (IC), and the total number of IC patient-days in excess of IC bed capacity . Our results show that uncertainties not directly related to the exit strategies are secondary, although they should still be considered in comprehensive analysis intended to inform policy makers . The sensitivity analysis discloses the crucial role of the intervention uptake by the population and of the capability to trace infected individuals . Finally, we explore the existence of a safe operating space . For Intermittent Lockdown we find only a small region in the model parameter space where the key indicators of the model stay within safe bounds, whereas this region is larger for the other exit strategies.