With the increasing demand for efficient, power-dense, and reliable power systems in aerospace applications, the thermal management of high-power electronic components has become a critical challenge. High-power common-mode chokes, which are essential components for electromagnetic interference (EMI) suppression, generate significant heat during operation, necessitating effective cooling techniques to maintain optimal performance and prolong their lifespan. This paper presents the design of a novel cylindrical jet impingement cooling system specifically tailored for high-power common-mode chokes in aerospace applications. The proposed cooling system leverages the advantages of jet impingement cooling to achieve enhanced heat transfer and temperature uniformity across the magnetic core as well as the bus bar. A cylindrical configuration is chosen to accommodate the geometric constraints of the magnetic core and bus bar configuration used in such applications. Mathematical modelling in partnership with computational fluid dynamics (CFD) simulations is employed to evaluate the thermal as well as pressure drop performance of the system.