  In an empirical Bayes analysis, we use data from repeated sampling to imitate
inferences made by an oracle Bayesian with extensive knowledge of the
data-generating distribution. Existing results provide a comprehensive
characterization of when and why empirical Bayes point estimates accurately
recover oracle Bayes behavior. In this paper, we develop flexible and practical
confidence intervals that provide asymptotic frequentist coverage of empirical
Bayes estimands, such as the posterior mean or the local false sign rate. The
coverage statements hold even when the estimands are only partially identified
or when empirical Bayes point estimates converge very slowly.
