ABSTRACT Compact binaries such as double neutron stars or a neutron star paired with a black hole, are strong sources of gravitational waves during coalescence and also the likely progenitors of various electromagnetic phenomena, notably short-duration gamma-ray bursts (SGRBs), and kilonovae. In this work, we generate populations of synthetic binaries and place them in galaxies from the large-scale hydrodynamical galaxy evolution simulation, eagle. With our zELDA code, binaries are seeded in proportion to star formation rate, and we follow their evolution to merger using both the bpass and cosmic binary stellar evolution codes. We track their dynamical evolution within their host galaxy potential, to estimate the galactocentric distance at the time of the merger. Finally, we apply observational selection criteria to allow comparison of this model population with the legacy sample of SGRBs. We find a reasonable agreement with the redshift distribution (peaking at 0.5 < z < 1), host morphologies, and projected galactocentric offsets (modal impact parameter ≲10 kpc). Depending on the binary simulation used, we predict $\sim 16\!-\!35{{\ \rm per\ cent}}$ of SGRB events would appear ‘host-less’, i.e. sources that merge with high impact parameters or have hosts fainter than the detection limit (H > 26).