A numerical procedure is outlined for obtaining an interval estimate of a parameter in an empirical Bayes estimation problem. The case where each observed value x has a binomial distribution, conditional on a parameter zeta, is the only case considered. For each x, the parameter estimated is the expected value of zeta given x. The main purpose is to throw some light on the effectiveness of empirical Bayes estimation in samples of various sizes. Illustrative numerical results are presented. (Author)