With the Stratospheric Observatory for Infrared Astronomy (SOFIA) routinely operating science flights, we demonstrate that observations with the Faint Object infraRed CAmera for the SOFIA Telescope (FORCAST) can provide reliable estimates of the internal luminosities, $L_{rm int}$, of protostars. We have developed a technique to estimate $L_{rm int}$ using a pair of FORCAST filters: one short-wavelength filter centered within 19.7-25.3 $mu$m, and one long-wavelength filter within 31.5-37.1 $mu$m. These $L_{rm int}$ estimates are reliable to within 30-40% for 67% of protostars and to within a factor of 2.3-2.6 for 99% of protostars. The filter pair comprised of F25.3$mu$m and F37.1$mu$m achieves the best sensitivity and most constrained results. We evaluate several assumptions that could lead to systematic uncertainties. The OH5 dust opacity matches observational constraints for protostellar environments best, though not perfectly; we find that any improved dust model will have a small impact of 5-10% on the $L_{rm int}$ estimates. For protostellar envelopes, the TSC84 model yields masses that are twice those of the Ulrich model, but we conclude this mass difference does not significantly impact results at the mid-infrared wavelengths probed by FORCAST. Thus, FORCAST is a powerful instrument for luminosity studies targeting newly discovered protostars or suspected protostars lacking detections longward of 24 $mu$m. Furthermore, with its dynamic range and greater angular resolution, FORCAST may be used to characterize protostars that were either saturated or merged with other sources in previous surveys using the Spitzer Space Telescope or Herschel Space Observatory.
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