This paper proposes a nets framework for studying robust parametric set membership identification. We derive some ner; results on the fundamental limitations of algorithms in this framework, given a particular model structure. The new idea is to quantify uncertainty only with respect to the (finite dimensional) parametric part of the model and not the (fixed size) unmodeled dynamics. Thus, the measure of uncertainty is different from the measures used in previous robust identification work where system norms are used to quantify uncertainty. As an example, the results are used to assess the fidelity of a certain approximate robust parametric set membership identification algorithm.