Wave energy converter (WEC) modelling attracts significant uncertainty, often due to the need to develop compact parametric models for simulation, optimisation and control design. For linear models, which form the basis of many WEC control philosophies, this uncertainty can be as a result of real system nonlinearity, particularly as a result of control action, as well as more general uncertainty in the hydrodynamic modelling process. Recent developments in WEC control include the development of robust control algorithms, which utilise a nominal linear model, but tolerate a level of uncertainty in the model parameters. This study develops a framework for identifying a nominal model plus model uncertainty bounds, which uses data from nonlinear computational fluid dynamics (CFD) simulation. Two robust control solutions are developed, one with an analytical approach, for circular uncertainty boundaries, and a further numerical approach, considering uncertainty sets of arbitrary shape. Finally, the comparative controller performance, based on the appropriate selection of a nominal model and uncertainty bound, compared to a non-robust nominal controller, is shown.