This paper is devoted to evaluating the quantification of uncertainty involved in the study of Aeolian vibrations of Optical Ground Wire (OPGW) cable systems installed on overhead power transmission lines. The Energy Balance Method (EBM) is widely used to estimate the severity of steady-state Aeolian vibrations. Although the EBM requires some experimental characterization of system parameters (as indicated by international Standards), it is necessary to mention that such a procedure is connected with uncertainties which makes it difficult for the proper homologation of the cable systems. In this article, the parametric probabilistic approach is employed to quantify the level of uncertainty associated with the EBM in the study of Aeolian vibrations of OPGW. The relevant parameters of the EBM (damper properties, cable self-damping, and the power imparted by the wind) are assumed as random variables whose distribution is deduced by means of the Maximum Entropy Principle. Then a Monte Carlo simulation is performed, and the input and output uncertainties are contrasted. Finally, a global sensitivity analysis is conducted to identify the Sobol' indices. Results indicate that parameters related to self-damping and damper are the most influential on uncertainty and output variability. In this sense, the present framework constitutes a powerful tool in the robust design of damper systems for OPGW cables.