We present a first systematic comparison of superluminous Type Ia supernovae (SNe Ia) at late epochs, including previously unpublished photometric and spectroscopic observations of SN 2007if, SN 2009dc and SNF20080723-012. Photometrically, the objects of our sample show a diverse late-time behaviour, some of them fading quite rapidly after a light-curve break at ∼ 150-200 d. The latter is likely the result of flux redistribution into the infrared, possibly caused by dust formation, rather than a true bolometric effect. Nebular spectra of superluminous SNe Ia are characterized by weak or absent Fe iii emission, pointing at a low ejecta ionization state as a result of high densities. To constrain the ejecta and 56Ni masses of superluminous SNe Ia, we compare the observed bolometric light curve of SN 2009dc with synthetic model light curves, focusing on the radioactive tail after ∼60 d. Models with enough 56Ni to explain the light-curve peak by radioactive decay, and at the same time sufficient mass to keep the ejecta velocities low, fail to reproduce the observed light-curve tail of SN 2009dc because of too much γ-ray trapping. We instead propose a model with ∼1 M of 56Ni and ∼2 M of ejecta, which may be interpreted as the explosion of a Chandrasekhar-mass white dwarf (WD) enshrouded by 0.6-0.7 M of C/O-rich material, as it could result from a merger of two massive C/O WDs. This model reproduces the late light curve of SN 2009dc well. A flux deficit at peak may be compensated by light from the interaction of the ejecta with the surrounding material.