  Locating ultra-cool companions to M dwarfs is important for constraining
low-mass formation models, the measurement of sub-stellar dynamical masses and
radii, and for testing ultra-cool evolutionary models. We present an optimised
method for identifying M dwarfs which may have unresolved ultra-cool
companions. We construct a catalogue of 440,694 candidates, from WISE, 2MASS
and SDSS, based on optical and near-infrared colours and reduced proper motion.
With strict reddening, photometric and quality constraints we isolate a
sub-sample of 36,898 M dwarfs and search for possible mid-infrared M dwarf +
ultra-cool dwarf candidates by comparing M dwarfs which have similar
optical/near-infrared colours (chosen for their sensitivity to effective
temperature and metallicity). We present 1,082 M dwarf + ultra-cool dwarf
candidates for follow-up. Using simulated ultra-cool dwarf companions to M
dwarfs, we estimate that the occurrence of unresolved ultra-cool companions
amongst our M dwarf + ultra-cool dwarf candidates should be at least four times
the average for our full M dwarf catalogue. We discuss possible contamination
and bias and predict yields of candidates based on our simulations.
