To increase power density and efficiency, it is ideal to minimize the size and power loss of components, including inductors. A standard inductor design technique is placing an air gap in the magnetic core, allowing designers to tune the inductance and allow higher levels of magnetic field without saturation. The inclusion of gaps can increase the total magnetic core loss beyond those predicted by common models such as the Steinmetz equation, creating the need for accurate gap loss models. In this study, the losses of a nanocrystalline inductor core are experimentally measured and compared to an existing gap loss model, showing significant agreement with predicted values. The model was then integrated into a multi-objective optimization framework to evaluate the fitness of nanocrystalline cores against ferrite cores at different switching frequencies. This work finds that gap losses can increase the total loss of nanocrystalline inductors by up to an order of magnitude as frequency increases, implying that consideration of gap losses is vital to selecting the appropriate core material for design applications.