Modeling of uncertain systems with normalized coprime factor description is investigated where the experimental data is given by a finite set of frequency response measurement samples of the open loop plant that is linear, time-invariant, and possibly infinite-dimensional. The objective is not only to identify the nominal model but also to quantify the modeling error with sup-norm bounds in frequency domain. The uncertainty to be identified and quantified is chosen as the nu-metric, proposed by Vinnicombe [43], because of its compatibility with H-infinity-based robust control. An algorithm is developed to model the normalized coprime factors of the given plant using techniques of discrete Fourier analysis (DFA) and balanced stochastic truncation (BST) and is shown to be robust in the presence of the worst case noise. Upper bounds are derived for the associated modeling error based on the minimum a priori information of the underlying model set and of the noise level in the measurement data. A simulation example is used to illustrate the effectiveness of the proposed algorithm.