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Runaway stars can result from core‐collapse supernovae in multiple stellar systems. If the supernova disrupts the system, the companion is ejected with its former orbital velocity. A clear identification of a runaway star can yield the time and place of the explosion, as well as orbital parameters of the pre‐supernova binary system. Previous searches have mostly considered O‐ and B‐type stars as runaway stars because they are always young in absolute terms (not much older than the lifetime of the progenitor) and can be detected up to larger distances. Here, we present a search for runaway stars of all spectral types. For late‐type stars, a young age can be inferred from the lithium test. We used  Gaia  data to identify and characterize runaway star candidates in nearby supernova remnants, obtained spectra of 39 stars with UVES at the VLT and HDS at the Subaru telescope, and found a significant amount of lithium in the spectra of six dwarf stars. We present the spectral analysis, including measurements of radial velocities, atmospheric parameters, and lithium abundances. Then, we estimate the ages of our targets from the Hertzsprung‐Russell diagram and, using the lithium test, present a selection of promising runaway star candidates and draw constraints on the number of ejected runaway stars compared to model expectations.

A search for runaway stars in 12 Galactic supernova remnants