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.
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