This paper is focused on the electromagnetic and structural design of high-speed synchronous reluctance (HS-SyR) machines. Both design aspects are equally taken into account due to high speed requirements. Two design procedures, both based on multi-objectives stochastic optimization algorithms (OA) and Finite Element Analysis (FEA), are presented and compared in terms of computational time and quality of the final result. The first design procedure combines an electromagnetic FEA with an analytical rotor structural design. The second procedure evaluates both electromagnetic and structural performance using FEA simulations within the optimization. The former approach needs a structural refinement stage of the rotor geometry. The latter gives rotor designs ready for manufacturing at the cost of increased computational resources. The two approaches have been investigated considering the rotor design of an 80.000 rpm SyR motor for aeronautical applications. Finally, a sensitivity analysis has been performed to identify which variables most affect structural performance and which parameters need tighter manufacturing tolerances.