Techniques of Armitage (1958) for finding confidence intervals after sequential tests (SCI) are applied to curtailed binomial test boundaries. The form of the exact randomized SCI is given. We also show that the conservative confidence interval calculated as though a fixed sample size procedure had been used (FCI) remains conservative when used after stopping on a curtailed boundary. Numerical results are obtained to assess the potential gains that may be obtained by using the conservative SCI or exact SCI over the conservative FCI for these boundaries.