Water resource system planning is complicated by uncertainty on the magnitude and direction of climate change. Therefore, developments such as new infrastructure or changed management rules that would work acceptably well under a diverse set of future conditions (i.e., robust solutions) are preferred. Robust multi-objective optimisation can help identify advantageous system designs which include existing infrastructure plus a selected subset of new interventions. The method evaluates options using simulated water resource performance metrics statistically aggregated to summarise performance over the climate scenario ensemble. In most cases such ‘robustness metrics’ are sensitive to scenarios under which the system performs poorly and so results may be strongly influenced by a minority of unfavorable climate scenarios. Understanding the influence of specific climate scenarios on robust optimised decision alternatives can help better interpret their results. We propose an automated multi-criteria design-under-uncertainty sensitivity analysis formulation that uses multi-objective evolutionary algorithms to reveal robust and efficient designs under different samples of a climate scenario ensemble. The method is applied to a reservoir management problem in the Rufiji River basin, Tanzania, which involves the second largest dam in Africa. We find that solutions optimised for robustness under alternative groups of climate scenarios exhibit important differences. This becomes particularly decision-relevant if analysts and/or decision-makers have differing confidence levels in the relevance of certain climate scenarios. The proposed approach motivates continued research on how climate model credibility should inform climate scenario selection because it demonstrates the influence scenario selection has on recommendations arising from robust optimisation design processes.