The desire to reduce gas turbine emissions drives the use of design optimization approaches within the combustor design process. However, the relative cost of combustion simulations can prohibit such optimizations from being carried out within an industrial setting. Strategies which can significantly reduce the cost of such studies can enable designers to further improve emissions performance. This paper investigates the application of a multifidelity surrogate modeling approach to the design optimization of a typical gas turbine combustor from a civil airliner engine. Results over three different case studies of varying problem dimensionality indicate that a multifidelity surrogate modeling-based design optimization, whereby the simulation fidelity is varied by adjusting the coarseness of the mesh, can indeed improve optimization performance. These results indicate that such an approach has the potential to significantly reduce design optimization cost while achieving similar, or in some cases superior, design performance.