We use the IllustrisTNG cosmological hydrodynamical simulations to investigate how the specific star formation rates (sSFRs) of massive galaxies (M * > 10 10 M ) depend on the distance to their closest companions. We estimate sSFR enhancements by comparing with control samples that are matched in redshift, stellar mass, local density and isolation, and we restrict our analysis to pairs with stellar mass ratios of 0.1 to 10. At small separations (∼ 15 kpc), the mean sSFR is enhanced by a factor of 2.0 ± 0.1 in the flagship (110.7 Mpc) 3 simulation (TNG100-1). Statistically significant enhancements extend out to 3D separations of 280 kpc in the (302.6 Mpc) 3 simulation (TNG300-1). We find similar trends in the EAGLE and Illustris simulations, although their sSFR enhancements are lower than those in TNG100-1 by about a factor of two. Enhancements in IllustrisTNG galaxies are seen throughout the redshift range explored (0 z < 1), with the strength of the enhancements decreasing with increasing redshift for galaxies with close companions. In order to more closely compare with observational results, we separately consider 2D projected distances between galaxies in IllustrisTNG. We detect significant sSFR enhancements out to projected separations of 260 kpc in TNG300-1, with projection effects diluting the size of the enhancements by about 20 per cent below 50 kpc. We find similar sSFR enhancements in TNG100-1 and Sloan Digital Sky Survey galaxies, with enhancements extending out to projected separations of about 150 kpc for star-forming galaxies at z < 0.2. Finally, by summing over all separations, we estimate that the presence of closest companions boosts the average sSFR of massive galaxies in TNG100-1 by 14.5 per cent.