Prior to the evaluation of protective efficacy, experimental vaccines conventionally undergo phase II randomized controlled clinical trials to evaluate safety and immunogenicity. Typically, an experimental vaccine is compared to another vaccine or to a placebo with respect to adverse events or immune responses, or both. Various strategies and methods are available for design and analysis of such studies. A key aspect of design is the determination of sample size. Often a sample size is chosen that gives a high probability ("power") of finding a statistically significant difference in an outcome of interest, if a difference of a specified size exists. This approach is appropriate when the primary goal of the study is to demonstrate that a difference exists between two groups or treatments. It may not, however, give adequate assurance that a confidence interval around the observed difference will be narrow enough to exclude the possibility of an unacceptably low immune response or unacceptably high adverse event frequency in recipients of the experimental vaccine. In this paper, we apply the "non-inferiority" trial design to phase II vaccine studies; that is, we design the trial to rule out a difference between the vaccine and control in immunogenicity or reactogenicity that is considered unacceptable. We also consider a setting in which the desire is to show that the difference between immune response rates for vaccine and control is greater than a specified value.