Sensitive spectroscopic techniques involving high-finesse Fabry-Perot resonators are widely used in the microwave and near-infrared spectral regimes, but hardware limitations have hindered their extension to far-infrared wavelengths. While there is no theoretical limit to the frequency region where cavity-enhanced techniques are practical, the sensitivity of these methods does depend explicitly on the availability of highly reflective optics and, in the case of cavity ringdown spectroscopy, sufficiently fast detectors. Here, we describe a novel high-finesse cavity that uses wire-grid polarizers as the reflective surfaces. Quality factors on the order of 10(5) are achieved at 250 GHz. Based on the optimized cavity design, we investigate the feasibility of extending the cavity ringdown technique to far-infrared wavelengths. With the present commercially available technology, we find spectrometer performance to be limited by both the available optics and detectors. With a 120 cm cavity and a detector response time of ~500 ns, we predict a minimum detectable absorption coefficient, αmin, on the order of 10(-7) cm(-1). Given the sensitivity and noise requirements for the ringdown measurements, faster and more sensitive detectors are needed before implementation of the spectrometer is practical or offers any significant advances to existing methods at far-infrared wavelengths.