Current computer systems and communication networks tend to be highly complex, and they typically hide their internal structure from their users. Thus, for selected aspects of capacity planning, overload control and related applications, it is useful to have a method allowing one to find good and relatively simple approximations for the observed system behavior with little knowledge of the system internal structure or operation. This paper investigates one such approach where we attempt to represent the observed behavior by adequately selecting the parameters of a set of queueing models. We identify a limited number of queueing models that we use as Building Blocks in our procedure. The selected Building Blocks allow us to accurately approximate the measured behavior of a range of different systems. The models used include a small selection of elementary queueing models, as well as original models of system congestion and saturation. We propose an approach for selecting suitable Building Blocks, as well as for their calibration. In particular, we automate the calibration step and make it systematic through the use of a Derivative- Free Optimization technique. We are able to successfully validate our methodology for a number of case studies. Finally, we discuss the potential and the limitations of the proposed approach.