This paper investigates how two-port network theory as a means for system identification can be applied to the analysis of brass instruments. A special focus is placed on the energy conversion efficiency as this is limited by inner damping, which receives much attention by expert players and makers of brasses. Theory suggests that a reconstruction of the 2 × 2 matrix representing the network requires input impedance and transfer function for two different boundary conditions. Besides the normal case of free sound radiation, instruments are also analyzed with the bell closed by a spherical cap. For this purpose, a customized 3D-printed spherical cap was fabricated and attached to the bell. Four measured spectra and the passivity condition over-determine the set of system equations. It is shown how to take advantage of this freedom when analyzing wind instruments. Measurements and simulations of a trumpet and a trombone are presented and compared.