A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference framework by Wasserman et al. (2020) and avoids using moment selection tuning parameters, resampling, or simulations. The method is designed for constructing confidence intervals for counterfactual objects and other functionals of the underlying parameter. It can be used in applications that involve model incompleteness, discrete and continuous covariates, and parameters containing nuisance components.