We present new measurements of projected rotation rates (v sin i) derived from high-resolution spectra of unevolved G and K field dwarfs (Kim et al. 2010) and previously unpublished spectra of low mass dwarfs in the Alpha Persei open cluster. These stars reside on the main sequence below the luminosities where isochrone fitting can determine stellar ages. We combine our v sin i measurements with stellar activity indicators and/or the presence of lithium to derive posterior distributions of stellar age (or upper limits on stellar age) for our sample and several other large spectroscopic surveys from the literature. Using parallaxes and proper motions retrieved from Gaia data release 2, we show that, regardless of the selection methods in these samples, stars with detectable rotation and lithium are members of kinematically cold populations as expected of young stars. We pay particular attention to the effect of uncertainties in v sin i on the calculation of the age posteriors, and we demonstrate that these are not significant compared to the effects of inclination angle except when v sin i is at or near the detection limit. Finally, we discuss how well this method can be implemented to identify the youngest exoplanet host stars from spectra alone.