The empirical “black-box” characterization of non-linear systems with memory is a complex problem which cannot be dealt with by means of a unique, general-purpose mathematical approach such as the Volterra series. In fact, from a metrological point of view, the feasibility and reliability of the measurement procedure must be the criterion on the basis of which any mathematical approach for modelling purposes must be evaluated. This paper describes different solutions for the behavioural identification of non-linear dynamic systems, all based on a modified Volterra series, which are characterized by a reduced number of operators with respect to the classical Volterra approach. The operator reduction, which does not affect the accuracy of the obtained models if a mild assumption on the system memory time duration is satisfied, allows a reliable extraction of the model parameters by means of conventional instrumentation, without the need for the generation of complicated input probing signals or additional approximations. A detailed discussion is provided in order to estimate when each of the proposed approaches can be practically used, by pointing out the hypotheses that must be taken into account in order to minimise the modified series truncation errors. Experimental examples, showing the validity of the proposed approaches, are given in the last section of the paper, as well as a comparison between the performances of the different solutions when applied to the important field of electron device characterization.