Abstract: The James Webb Space Telescope (JWST) will provide unprecedented spectroscopic observations of extrasolar planets, including mid-infrared spectra using MIRI. Many target objects at these wavelengths will be giant planets observed by direct imaging. However, the techniques to analyze these spectra have not yet been explored in depth. Brown dwarfs and especially stellar companions provide an analog for giant planets, with many similar properties, which can be used to develop these techniques. We use the spectral retrieval code APOLLO to retrieve atmospheric parameters from mid-infrared spectra taken by the Spitzer Space Telescope for the brown dwarf companions GJ 570D, HN Peg B, and Wolf 940B. By comparing the results of these retrievals with those of ground-based near-infrared spectra, we infer bulk properties and atmospheric compositions for these objects. We discuss the implications of these results for both optimizing and interpreting JWST observations of giant exoplanets.