The role of experimental nonlinear dynamics in the proper reduced-order modeling of an elastic suspended cable undergoing finite-amplitude vibrations is analyzed. Two main aspects of the problem are addressed, namely (i) the number of discretizing functions to be used in a low-order finite-degree-of-freedom theoretical model in order to detect the main features of the observed nonlinear regimes, and (ii) the capability of different orthonormal function bases employed in a specific reduced-order model to reproduce complex regimes and bifurcation scenarios. Based on results of in-depth experimental investigations of a quasiperiodic scenario to chaos in a cable/mass system, a three-degree-of-freedom model of suspended cable is formulated, and different truncated bases of approximating functions are considered. They include standard linear normal modes, and proper orthogonal modal functions obtained from variable sets of experimental proper orthogonal modes identified in different intervals of the frequency range wherein the quasiperiodic scenario develops. The performances of the ensuing discretized models and their capability to qualitatively detect some main features of the actual regular and nonregular experimental responses are investigated through computer simulations.