Accurate astrophysical polarimetry requires a proper characterization of the polarization properties of the telescope and instrumentation employed to obtain the observations. Determining the telescope and instrument Muller matrix is becoming increasingly difficult with the increase in aperture size, precision requirements and instrument complexity of new and upcoming projects. We have carried out a detailed multi-wavelength characterization of the Dunn Solar Telescope (DST) at the National Solar Observatory/Sacramento Peak as a case study and explore various possibilites for the determination of its polarimetric properties. We show that the telescope model proposed in this paper is more suitable than that in previous work in that it describes better the wavelength dependence of aluminum-coated mirrors. We explore the adequacy of the degrees of freedom allowed by the model using a novel mathematical formalism. Finally, we investigate the use of polarimeter calibration data taken at different times of the day to characterize the telescope and find that very valuable information on the telescope properties can be obtained in this manner. The results are also consistent with the entrance window polarizer measurements. This general method opens interesting possibilities for the calibration of future large-aperture telescopes and precision polarimetric instrumentation.