This dissertation investigates the use of gas turbine (GT) engine integrated solid oxide fuel cells (SOFCs) to reduce fuel burn in aircraft with large electrical loads like sensor-laden unmanned air vehicles (UAVs). The concept offers a number of advantages: the GT absorbs many SOFC balance of plant functions (supplying fuel, air, and heat to the fuel cell) thereby reducing the number of components in the system; the GT supplies fuel and pressurized air that significantly increases SOFC performance; heat and unreacted fuel from the SOFC are recaptured by the GT cycle offsetting system-level losses; good transient response of the GT cycle compensates for poor transient response of the SOFC. The net result is a system that can supply more electrical power more efficiently than comparable engine-generator systems with only modest (<10%) decrease in power density. Thermodynamic models of SOFCs, catalytic partial oxidation (CPOx) reactors, and three GT engine types (turbojet, combined exhaust turbofan, separate exhaust turbofan) are developed that account for equilibrium gas phase and electrochemical reaction, pressure losses, and heat losses in ways that capture `down-the-channel' effects (a level of fidelity necessary for making meaningful performance, mass, and volume estimates). Models are created in a NASA-developed environment called Numerical Propulsion System Simulation (NPSS). A sensitivity analysis identifies important design parameters and translates uncertainties in model parameters into uncertainties in overall performance. GT-SOFC integrations reduce fuel burn 3-4% in 50 kW systems on 35 kN rated engines (all types) with overall uncertainty <1%. Reductions of 15-20% are possible at the 200 kW power level. GT-SOFCs are also able to provide more electric power (factors >3 in some cases) than generator-based systems before encountering turbine inlet temperature limits. Aerodynamic drag effects of engine-airframe integration are by far the most important limiter of the combined propulsion/electrical generation concept. However, up to 100-200 kW can be produced in a bypass ratio = 8, overall pressure ratio = 40 turbofan with little or no drag penalty. This study shows that it is possible to create cooperatively integrated GT-SOFC systems for combined propulsion and power with better overall performance than stand-alone components.