AbstractIt is expected that most massive stars have companions and thus that some core-collapse supernovae should have a runaway companion. The precise astrometry and photometry provided by Gaia allows for the systematic discovery of these runaway companions. We combine a prior on the properties of runaway stars from binary evolution with data from TGAS and APASS to search for runaway stars within ten nearby supernova remnants. We strongly confirm the existing candidate HD 37424 in S147, propose the Be star BD+50 3188 to be associated with HB 21, and suggest tentative candidates for the Cygnus and Monoceros Loops.