This paper describes the implementation of a structural health monitoring (SHM) method for mechanical components and structures in composite materials with a focus on carbon-fiber-overwrapped pressure vessels (COPVs) used in the aerospace industry. Two flex arrays of polyvinylidene fluoride (PVDF) interdigital transducers have been designed, realized, and mounted on the COPV to generate guided Lamb waves (mode A0) for damage assessment. We developed a custom electronic instrument capable of performing two functions using the same transducers: passive-mode detection of impacts and active-mode damage assessment using Lamb waves. The impact detection is based on an accurate evaluation of the time of arrival and was successfully tested with low-velocity impacts (7 and 30 J). Damage detection and progression is based on the calculation of a damage index matrix which compares a set of signals acquired from the transducers with a baseline. This paper also investigates the advantage of tuning the active-mode frequency to obtain the maximum transducer response in the presence of structural variations of the specimen, and therefore, the highest sensitivity to damage.