The statistic of interest in the economic evaluation of health care interventions is the incremental cost effectiveness ratio (ICER), which is defined as the difference in cost between two treatment interventions over the difference in their effect. Where patient-specific data on costs and health outcomes are available, it is natural to attempt to quantify uncertainty in the estimated ICER using confidence intervals. Recent articles have focused on parametric methods for constructing confidence intervals. In this paper, we describe the construction of non-parametric bootstrap confidence intervals. The advantage of such intervals is that they do not depend on parametric assumptions of the sampling distribution of the ICER. We present a detailed description of the non-parametric bootstrap applied to data from a clinical trial, in order to demonstrate the strengths and weaknesses of the approach. By examining the bootstrap confidence limits successively as the number of bootstrap replications increases, we conclude that percentile bootstrap confidence interval methods provide a promising approach to estimating the uncertainty of ICER point estimates. However, successive bootstrap estimates of bias and standard error suggests that these may be unstable; accordingly, we strongly recommend a cautious interpretation of such estimates.