  We present new 0.9-2.45 $\mu$m spectroscopy ($R \sim 1000$), and $Y$, $J$,
$H$, $K_s$, $L^\prime$ photometry, obtained at Gemini North, of three low-mass
brown dwarf companions on wide orbits around young stars of the Upper Scorpius
OB association: HIP 78530 B, [PGZ2001] J161031.9-191305 B, and GSC 06214-00210
B. We use these data to assess the companions' spectral type, temperature,
surface gravity and mass, as well as the ability of the BT-Settl and
Drift-Phoenix atmosphere models to reproduce the spectral features of young
substellar objects. For completeness, we also analyze the archival spectroscopy
and photometry of the Upper Scorpius planetary mass companion 1RXS
J160929.1-210524 b. Based on a comparison with model spectra we find that the
companions, in the above order, have effective temperatures of 2700, 2500, 2300
and 1700 K. These temperatures are consistent with our inferred spectral types,
respectively M7 $\beta$, M9 $\gamma$, M9 $\gamma$, and L4 $\gamma$. From
bolometric luminosities estimated from atmosphere model spectra adjusted to our
photometry, and using evolution models at 5-10 Myr, we estimate masses of
21-25, 28-70, 14-17 and 7-12 $M_{\rm Jup}$, respectively. J1610-1913 B appears
significantly over-luminous for its inferred temperature, which explains its
higher mass estimate. Synthetic spectra based on the BT-Settl and Drift-Phoenix
atmosphere models generally offer a good fit to our observed spectra, although
our analysis has highlighted a few problems. For example, the best fits in the
individual near-infrared bands occur at different model temperatures. Also,
temperature estimates based on a comparison of the broadband magnitudes and
colors of the companions to synthetic magnitudes from the models are
systematically lower than the temperature estimates based on a comparison with
synthetic spectra.
