  Pair-instability supernovae (PISNe) are very luminous explosions of massive,
low metallicity stars. They can potentially be observed out to high redshifts
due to their high explosion energies, thus providing a probe of the Universe
prior to reionization. The near-infrared camera, NIRCam, on board the James
Webb Space Telescope is ideally suited for detecting their redshifted
ultraviolet emission. We calculate the photometric signature of high-redshift
PISNe and derive the optimal detection strategy for identifying their prompt
emission and possible afterglow. We differentiate between PISNe and other
sources that could have a similar photometric signature, such as active
galactic nuclei or high-redshift galaxies. We demonstrate that the optimal
strategy, which maximizes the visibility time of the PISN lightcurve per
invested exposure time, consists of the two wide-band filters F200W and F356W
with an exposure time of 600s. For such exposures, we expect one PISN at $z
\lesssim 7.5$ per at least 50,000 different field of view, which can be
accomplished with parallel observations and an extensive archival search. The
PISN afterglow, caused by nebular emission and reverberation, is very faint and
requires unfeasibly long exposure times to be uniquely identified. However,
this afterglow would be visible for several hundred years, about two orders of
magnitude longer than the prompt emission, rendering PISNe promising targets
for future, even more powerful telescopes.
