Non-minimum phase zeros and poles of a process put upper and lower constraints on the bandwidth of a closed loop system. It is thus of great interest to be able to identify these quantities. In this contribution it is shown that non-minimum phase zeros and unstable poles can be identified using high order models without the standard o(n) (n is the model order) variance penalty for over modeling. An asymptotic, in the model order and the number of data, expression for the variance of non-minimum phase zeros is derived. This result shows that the problem of determining the performance limits of a system from experimental data is considerably easier than identifying the complete system. As a direct application of this an optimal experiment design problem for identification of performance limits is posed and solved.