We investigate robust decision-making under utility uncertainty, using the maximin criterion, which optimizes utility for the worst case setting. We show how it is possible to efficiently compute the maximin optimal recommendation in face of utility uncertainty, even in large configuration spaces. We then introduce a new decision criterion, setwise maximin utility (SMMU), for constructing optimal recommendation sets: we develop algorithms for computing SMMU and present experimental results showing their performance. Finally, we discuss the problem of elicitation and prove (analogously to previous results related to regret-based and Bayesian elicitation) that SMMU leads to myopically optimal query sets.