Gas turbine engines include an engine frame defining an inner radial surface, a shaft rotatably mounted in the engine frame along a longitudinal axis, and an electric machine that includes a rotor coupled to the shaft and a stator coupled to the engine frame and defining an outer radial surface. In some gas turbine engines, the engine frame includes inlet and outlet fluid passages, each extending to a portion of the inner radial surface. The portion of the inner radial surface of the engine frame is spaced from the outer radial surface of the stator to form an annular fluid passage around the stator of an electric machine. The annular fluid passage is configured to direct a cooling fluid around the stator to remove heat from the stator. Some gas turbine engines include two or more positioning keys configured to fix the stator relative to the engine frame.