We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris, 1983b) may substantially undercover when this assumption is violated, and we derive a simple rule of thumb for gauging the potential coverage distortion. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least 1−α on average across the n EBCIs for each of the means. Our empirical applications consider effects of U.S. neighborhoods on intergenerational mobility, and structural changes in a large dynamic factor model for the Eurozone.