  Accretion onto 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$\gtrsim$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 (AD) 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 infra-red colour spaces designed to
select super-Eddington SEDs in both wide-field surveys (e.g., using SDSS, 2MASS
and WISE) and deep & 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 onto SMBHs at early cosmic epochs.
