Coronal mass ejections (CMEs) are eruptive events that cause a solar-type star to shed mass and magnetic flux. CMEs tend to occur together with flares, radio storms, and bursts of energetic particles. On the Sun, CME-related mass loss is roughly an order of magnitude less intense than that of the background solar wind. However, on other types of stars, CMEs have been proposed to carry away much more mass and energy than the time-steady wind. Earlier papers have used observed correlations between solar CMEs and flare energies, in combination with stellar flare observations, to estimate stellar CME rates. This paper sidesteps flares and attempts to calibrate a more fundamental correlation between surface-averaged magnetic fluxes and CME properties. For the Sun, there exists a power-law relationship between the magnetic filling factor and the CME kinetic energy flux, and it is generalized for use on other stars. An example prediction of the time evolution of wind/CME mass-loss rates for a solar-mass star is given. A key result is that for ages younger than about 1 Gyr (i.e., activity levels only slightly higher than the present-day Sun), the CME mass loss exceeds that of the time-steady wind. At younger ages, CMEs carry 10-100 times more mass than the wind, and such high rates may be powerful enough to dispel circumstellar disks and affect the habitability of nearby planets. The cumulative CME mass lost by the young Sun may have been as much as 1% of a solar mass.