Public policy makers use cost effectiveness analyses (CEAs) to decide which health and social care interventions to provide. Missing data are common in CEAs, but most studies use complete-case analysis. Appropriate methods have not been developed for handling missing data in complex settings, exemplified by CEAs that use data from cluster randomized trials. We present a multilevel multiple-imputation approach that recognizes the hierarchical structure of the data and is compatible with the bivariate multilevel models that are used to report cost effectiveness. We contrast this approach with single-level multiple imputation and complete-case analysis, in a CEA alongside a cluster randomized trial. The paper highlights the importance of adopting a principled approach to handling missing values in settings with complex data structures.