  We utilise theoretical models of Population III stellar+nebular spectra to
investigate the prospects of observing and accurately identifying Population
III galaxies with JWST using both deep imaging and spectroscopy. We investigate
a series of different colour cuts, finding that a combination of NIRCam and
MIRI photometry through the F444W-F560W, F560W-F770W colours offers the most
robust identifier of potential $z=8$ Pop III candidates. We calculate that
NIRCam will have to reach $\sim$28.5-30.0 AB mag depths (1-20 h), and MIRI
F560W must reach $\sim$27.5-29.0 AB mag depths (10-100 h) to achieve $5\sigma$
continuum detections of $M_* = 10^6~\mathrm{M}_\odot$ Pop III galaxies at
$z=8$. We also discuss the prospects of identifying Pop III candidates through
slitless and NIRSpec spectroscopic surveys that target Ly$\alpha$, H$\beta$
and/or He II $\lambda 1640$. We find small differences in the H$\beta$
rest-frame equivalent width (EW) between Pop III and non-Pop III galaxies,
rendering this diagnostic likely impractical. Instead, we find that the
detection of high EW He II $\lambda 1640$ emission will serve as the definitive
Pop III identifier, requiring (ultra-)deep integrations (10-250 h) with
NIRSpec/G140M for $M_*=10^6~\mathrm{M}_\odot$ Pop III galaxies at $z=8$.
However, MIRI F770W detections of Pop III galaxies will require substantial
gravitational lensing ($\mu=10$) and/or fortuitous imaging of exceptionally
massive ($M_* = 10^7~\mathrm{M}_\odot$) Pop III galaxies. Thus, NIRCam
medium-band imaging surveys that can search for high EW He II $\lambda 1640$
emitters in photometry may perhaps be a viable alternative for finding Pop III
candidates.
