Using resolved stellar photometry measured from archival Hubble Space Telescope imaging, we generate color-magnitude diagrams of the stars within 50 pc of the locations of historic core-collapse supernovae (SNe) that took place in galaxies within 8 Mpc. We fit these color-magnitude distributions with stellar evolution models to determine the best-fit age distribution of the young population. We then translate these age distributions into probability distributions for the progenitor mass of each SN. The measurements are anchored by the main-sequence stars surrounding the event, making them less sensitive to assumptions about binarity, post-main-sequence evolution, or circumstellar dust. We demonstrate that, in cases where the literature contains masses that have been measured from direct imaging, our measurements are consistent with (but less precise than) these measurements. Using this technique, we constrain the progenitor masses of 17 historic SNe, 11 of which have no previous estimates from direct imaging. Our measurements still allow the possibility that all SN progenitor masses are <20 M_{sun}_. However, the large uncertainties for the highest-mass progenitors also allow the possibility of no upper-mass cutoff.