ABSTRACT Comparison of theoretical line profiles to observations provides important tests for supernova explosion models. We study the shapes of radioactive decay lines predicted by current 3D core-collapse explosion simulations, and compare these to observations of SN 1987A and Cas A. Both the widths and shifts of decay lines vary by several thousand kilometres per second depending on viewing angle. The line profiles can be complex with multiple peaks. By combining observational constraints from 56Co decay lines, 44Ti decay lines, and Fe IR lines, we delineate a picture of the morphology of the explosive burning ashes in SN 1987A. For MZAMS = 15−20 M⊙ progenitors exploding with ∼1.5 × 1051 erg, ejecta structures suitable to reproduce the observations involve a bulk asymmetry of the 56Ni of at least ∼400 km s−1 and a bulk velocity of at least 1500 km s−1. By adding constraints to reproduce the UVOIR bolometric light curve of SN 1987A up to 600 d, an ejecta mass around 14 M⊙ is favoured. We also investigate whether observed decay lines can constrain the neutron star (NS) kick velocity. The model grid provides a constraint VNS > Vredshift, and applying this to SN 1987A gives a NS kick of at least 500 km s−1. For Cas A, our single model provides a satisfactory fit to the NuSTAR observations and reinforces the result that current neutrino-driven core-collapse SN models achieve enough bulk asymmetry in the explosive burning material. Finally, we investigate the internal gamma-ray field and energy deposition, and compare the 3D models to 1D approximations.