AbstractIn a recent paper, it has been shown that, if an N‐port network fulfills the condition of (geometrical) unconditional stability at a given frequency, then its scattering parameters will also necessarily satisfy N easily computable bounds, one per port. In order to complete that picture, this contribution investigates whether a tighter bound can be obtained by combining the bounds into just one. The answer is in general negative, except that the 3‐port case does indeed exhibit a peculiar behavior: this can be exploited to reduce the upper bound when the diagonal elements of the scattering matrix are limited in magnitude up to some , and in particular for (simultaneous conjugate match).