  Knowledge of late K and M dwarf metallicities can be used to guide planet
searches and constrain planet formation models. However, the determination of
metallicities of late-type stars is difficult because visible wavelength
spectra of their cool atmospheres contain many overlapping absorption lines,
preventing the measurement of equivalent widths. We present new methods, and
improved calibrations of existing methods, to determine metallicities of late-K
and M dwarfs from moderate resolution (1300 < R < 2000) visible and infrared
spectra. We select a sample of 112 wide binary systems that contain a late-type
companion to a solar-type primary star. Our sample includes 62 primary stars
with previously published metallicities, as well as 50 stars with metallicities
determined from our own observations. We use our sample to empirically
determine which features in the spectrum of the companion are best correlated
with the metallicity of the primary. We derive metallicity calibrations for
different wavelength ranges, and show that it is possible to get metallicities
reliable to < 0.10 dex using either visible, J, H, or K band spectra. Our
calibrations are applicable to dwarfs with metallicities of -1.04 < [Fe/H]<
+0.56 and spectral types from K7 to M5. Lastly, we use our sample of wide
binaries to test and refine existing calibrations to determine M dwarf
metallicities. We find that the zeta parameter, which measures the ratio of TiO
can CaH bands, is correlated with [Fe/H] for super-solar metallicities, and
zeta does not always correctly identify metal-poor M dwarfs. We also find that
existing calibrations in the K and H band are quite reliable for stars with
[Fe/H] > -0.5, but are less useful for more metal-poor stars.
