  We present spectroscopic determinations of the effective temperatures,
surface gravities and metallicities for 21 M-dwarfs observed at high-resolution
(R $\sim$ 22,500) in the \textit{H}-band as part of the SDSS-IV APOGEE survey.
The atmospheric parameters and metallicities are derived from spectral
syntheses with 1-D LTE plane parallel MARCS models and the APOGEE
atomic/molecular line list, together with up-to-date H$_{2}$O and FeH molecular
line lists. Our sample range in $T_{\rm eff}$ from $\sim$ 3200 to 3800K, where
eleven stars are in binary systems with a warmer (FGK) primary, while the other
10 M-dwarfs have interferometric radii in the literature. We define an
$M_{K_{S}}$--Radius calibration based on our M-dwarf radii derived from the
detailed analysis of APOGEE spectra and Gaia DR2 distances, as well as a
mass-radius relation using the spectroscopically-derived surface gravities. A
comparison of the derived radii with interferometric values from the literature
finds that the spectroscopic radii are slightly offset towards smaller values,
with $\Delta$ = -0.01 $\pm$ 0.02 $R{\star}$/$R_{\odot}$. In addition, the
derived M-dwarf masses based upon the radii and surface gravities tend to be
slightly smaller (by $\sim$5-10\%) than masses derived for M-dwarf members of
eclipsing binary systems for a given stellar radius. The metallicities derived
for the 11 M-dwarfs in binary systems, compared to metallicities obtained for
their hotter FGK main-sequence primary stars from the literature, shows
excellent agreement, with a mean difference of [Fe/H](M-dwarf - FGK primary) =
+0.04 $\pm$ 0.18 dex, confirming the APOGEE metallicity scale derived here for
M-dwarfs.
