In this paper we treat a general worst-case system identification problem. This problem is worst-case with respect to both noise and system modeling uncertainty. We consider this problem under various a priori information structures. We determine bounds on the minimum duration identification experiment that must be run to identify the plant to within a specified guaranteed worst-case error bound. Our results are algorithm independent. We show that this minimum duration is prohibitively long. Based on our results, we suggest that worst-case (with respect to noise) system identification requires unrealistic amounts of experimental data.