The design of gas turbine combustors is an iterative process which is often limited by the available modelling tools. While high degrees of modelling accuracy have been achieved using high fidelity tools, these are computationally expensive and not appropriate for design space exploration. By contrast, reduced order models carry low computational expense, but cannot fully reconstruct the combustion problem which spans multiple branches of physics and is characterised by 3D phenomena. As a result, empirical correlations are often relied upon, but these limit the designer to a narrow range of validity, preventing the exploration of novel design solutions.To facilitate the design of new low emissions combustors, for which empirical models are not valid, a multi-fidelity design process has been followed. In this process, physics-based low order models are built; calibrated by high fidelity simulations and then used in multi-objective optimisation studies. This provides detailed insight early in the design process, leading to more fruitful optimisation studies and a shorter design cycle. This approach has been successfully demonstrated on other turbomachinary sub-systems, but has not yet been applied to combustors using publicly available methods.In the current work, the multi-fidelity design process is demonstrated on the design and analysis of an impingement/effusion cooling layout for a lean direct injection combustor liner. A novel mutli-fidelity methodology was followed which used only publicly available methods. By following this approach, an indication of liner wall temperature distributions could be obtained very early in the design process, prior to any prototyping or testing. As such, applying a mutli-fidelity design approach to gas turbine combustors was shown to be both feasible and beneficial.The results from the high fidelity simulations were compared to those of the low order model, revealing a number of discrepancies due to physics not captured - most notably a strong interaction between the swirling flow and liner wall. These detailed interactions resulted in failure of the initial cooling layout, leading to the liner exceeding its limit temperature by 10%. Inclusion of models to predict these phenomena have been recommended to improve the low order code fidelity. In doing so, the multi-fidelity modelling loop will be closed, yielding a more capable design code to be used for executing design space exploration.