We observe the brightest member of the Praesepe cluster, ϵ Cnc, to precisely measure the characteristics of the stars in this binary system, en route to a new measurement of the cluster’s age. We present spectroscopic radial velocity measurements and interferometric observations of the sky-projected orbit to derive the masses, which we find to be M 1/M ⊙ = 2.420 ± 0.008 and M 2/M ⊙ = 2.226 ± 0.004. We place limits on the color–magnitude positions of the stars by using spectroscopic and interferometric luminosity ratios while trying to reproduce the spectral energy distribution of ϵ Cnc. We reexamine the cluster membership of stars at the bright end of the color–magnitude diagram using Gaia data and literature radial velocity information. The binary star data are consistent with an age of 637 ± 19 Myr, as determined from MIST model isochrones. The masses and luminosities of the stars appear to select models with the most commonly used amount of convective core overshooting.