We present near-infrared (1.0-2.4 micron) spectra confirming the youth and cool effective temperatures of 6 brown dwarfs and low mass stars with circumstellar disks toward the Chamaeleon II and Ophiuchus star forming regions. The spectrum of one of our objects indicates that it has a spectral type of ~L1, making it one of the latest spectral type young brown dwarfs identified to date. Comparing spectra of young brown dwarfs, field dwarfs, and giant stars, we define a 1.49-1.56 micron H2O index capable of determining spectral type to within 1 sub-type, independent of gravity. We have also defined an index based on the 1.14 micron sodium feature that is sensitive to gravity, but only weakly dependent on spectral type for field dwarfs. Our 1.14 micron Na index can be used to distinguish young cluster members (t <~ 5 Myr) from young field dwarfs, both of which may have the triangular H-band continuum shape which persists for at least tens of Myr. Using effective temperatures determined from the spectral types of our objects along with luminosities derived from near and mid-infrared photometry, we place our objects on the H-R diagram and overlay evolutionary models to estimate the masses and ages of our young sources. Three of our sources have inferred ages (t ~= 10-30 Myr) significantly older than the median stellar age of their parent clouds (1-3 Myr). For these three objects, we derive masses ~3 times greater than expected for 1-3 Myr old brown dwarfs with the bolometric luminosities of our sources. The large discrepancies in the inferred masses and ages determined using two separate, yet reasonable methods, emphasize the need for caution when deriving or exploiting brown dwarf mass and age estimates.
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