Given a series of intrinsic features of structural glass systems (i.e., material properties, type of restraints, operational conditions, etc.), special care should be spent at the design stage, to ensure appropriate fail-safe requirements, but also in the service life of these innovative building components and assemblies. In this paper, the dynamic characterization of simple monolithic glass elements is presented, based on non-destructive laboratory experiments and Operational Modal Analysis (OMA) techniques, including Finite Element (FE) numerical simulations, classical analytical models, and video-tracking approaches. It is shown, in particular, how the actual restraint condition (i.e., flexibility of supports, with respect to ideal boundaries) can affect the vibration parameters of a given glass member (frequency and damping capacity). This turns out in possible variations of its overall structural performance, including stress-strain-related effects, hence suggesting the need for even further dedicated studies and methods for the reliable analysis and design of structural glass assemblies and complex systems under dynamic loads.