As commercial space travel increases, the need for reliable structural health monitoring to predict possible weaknesses or failures of structural materials also increases. Monitoring of polymer-based materials may be achieved through the use of dielectric spectroscopy by comparing permittivity or conductivity measurements performed on a sample in use to that of a pristine sample. Changes in these measured values or of the relaxation frequencies, if present, can indicate chemical or physical changes occurring within the material and the possible need for maintenance/replacement. In this work, we established indicative trends that occur in the dielectric spectra during accelerated aging of various high-performance polymeric materials (EVOH, PEEK, PPS, and UHMWPE). Uses for these materials range from electrical insulation and protective coatings to windows and air- or space-craft parts that may be subject to environmental damage over long-term operation. Accelerated thermal aging and ultraviolet/water-spray cyclic aging were performed in order to investigate the degradation of the aforementioned material. The Havriliak-Negami model was used in the analysis of the measured dielectric spectra in order to obtain the characteristic fit parameters from which aging-related trends were identified. With reference to the literature and from measured FTIR spectra, observations were connected to the underlying mechanisms causing the dielectric relaxations.