This paper details the weight optimization of the electrical machine required for an Airborne Wind Turbine (AWT) system. Presented investigations include the analysis of the powerto-weight ratio versus efficiency limits, γ-η Pareto fronts, of radial and axial flux machine topologies, by making use of analytical models, describing the electromagnetic and thermal behaviour. A direct search method is employed rather than a cost function minimization algorithm, as the analytical models allow the evaluation of the whole design space in a computationally efficient manner. The results reveal that the best performance in this case is achieved with a radial flux machine with an internal rotor where the magnets are arranged in a Halbach configuration. Including the weight of electromagnetically inactive parts, such as bearings, shaft and housing, a power-to-weight ratio of γ ≈ 6.2 kW/kg (2.8 kW/lb), at an efficiency of η ≈ 96 %, and a rated speed of 3200 r/min is achieved.