ABSTRACT Accretion on to black holes at rates above the Eddington limit has long been discussed in the context of supermassive black hole (SMBH) formation and evolution, providing a possible explanation for the presence of massive quasars at high redshifts (z ≳ 7), as well as having implications for SMBH growth at later epochs. However, it is currently unclear whether such ‘super-Eddington’ accretion occurs in SMBHs at all, how common it is, or whether every SMBH may experience it. In this work, we investigate the observational consequences of a simplistic model for super-Eddington accretion flows – an optically thick, geometrically thin accretion disc where the inner-most parts experience severe photon-trapping, which is enhanced with increased accretion rate. The resulting spectral energy distributions (SEDs) show a dramatic lack of rest-frame UV, or even optical, photons. Using a grid of model SEDs spanning a wide range in parameter space (including SMBH mass and accretion rate), we find that large optical quasar surveys (such as SDSS) may be missing most of these luminous systems. We then propose a set of colour selection criteria across optical and infrared colour spaces designed to select super-Eddington SEDs in both wide-field surveys (e.g. using SDSS, 2MASS, and WISE) and deep and narrow-field surveys (e.g. COSMOS). The proposed selection criteria are a necessary first step in establishing the relevance of advection-affected super-Eddington accretion on to SMBHs at early cosmic epochs.