  We present the results of a coordinated campaign to simultaneously observe
the M star binary Ross 733 simultaneously in the optical and near-ultraviolet
(NUV) with TESS and Swift respectively. We observed two flares in the Swift NUV
light curve. One of these was decay phase of a flare that was also detected
with TESS and the other was only detected in the NUV. We used the TESS light
curve to measure the white-light flare rate of Ross 733, and calculate that the
system flares with an energy of $10^{33}$ erg once every 1.5 days. We used our
simultaneous observations to measure a pseudo-continuum temperature of
$7340^{+810}_{-900}$K during the flare decay. We also used our observations to
test the NUV predictions of the 9000 K blackbody flare model, and find that it
underestimates number of flares we detect in our Swift NUV light curve. We
discuss the reasons for this and attribute it to the unaccounted contributions
from emission lines and continuum temperatures above 9000 K. We discuss how
additional observations are required to break the degeneracy between the two in
future multi-wavelength flare campaigns.
