We discuss the construction of asymptotic simultaneous upper confidence limits that jointly bound relative risks formed by comparing several treatments to a control. Motivated by a vaccine study, we investigate the performance of several methods under such settings. Inverting the minimum of score statistics, together with estimating the correlation matrix of these statistics under the null gives simultaneous coverage rates closest to the nominal level. In typical settings of vaccine studies, this method proves to be the most powerful of the ones considered, but computationally simpler alternatives are also worth exploring when the number of comparisons is large. Simultaneous lower and two-sided confidence intervals are also considered. All procedures can be implemented and evaluated using freely available and general R code. Copyright © 2010 John Wiley & Sons, Ltd.