We present a new cavity-based polarimetric scheme for highly sensitive and time-resolved measurements of birefringence and dichroism, linear and circular, that employs rapidly pulsed single-frequency continuous wave (CW) laser sources and extends current cavity-based spectropolarimetric techniques. We demonstrate how the use of a CW laser source allows for gains in spectral resolution, signal intensity, and data acquisition rate compared to traditional pulsed-based cavity ring-down polarimetry (CRDP). We discuss a particular CW-CRDP modality that is different from intensity-based cavity-enhanced polarimetric schemes as it relies on the determination of the polarization rotation frequency during a ring-down event generated by large intracavity polarization anisotropies. We present the principles of CW-CRDP and validate the applicability of this technique for the measurement of the non-resonant Faraday effect in solid SiO2 and CeF3 and gaseous butane. We give a general analysis of the fundamental sensitivity limits for CRDP techniques and show how the presented frequency-based methodology alleviates the requirement for high finesse cavities to achieve high polarimetric sensitivities and, thus, allows for the extension of cavity-based polarimetric schemes into different spectral regimes, but most importantly renders the CW-CRDP methodology particularly suitable for robust portable polarimetric instrumentations.