It is common practice to assess the passivity properties of rational macromodels via the eigenvalues of a particular Hamiltonian matrix that is established from the model's statespace representation. The size of the test matrix is equal to twice the number of states, which can make the eigenvalue computation time consuming in the case of large models. In this paper we explore the application of a half-size test matrix that was recently introduced for use with scattering (S-) parameter models. The new test matrix is shown to reduce the computation time by a factor of about eight, and it avoids the need for thresholding when processing the eigenvalues. ©2009 IEEE.