We present far-infrared polarimetry observations of M82 at 53 and 154 μm and NGC 253 at 89 μm, which were taken with High-resolution Airborne Wideband Camera-plus (HAWC+) in polarimetry mode on the Stratospheric Observatory for Infrared Astronomy. The polarization of M82 at 53 μm clearly shows a magnetic field geometry perpendicular to the disk in the hot dust emission. For M82 the polarization at 154 μm shows a combination of field geometry perpendicular to the disk in the nuclear region, but closer to parallel to the disk away from the nucleus. The fractional polarization at 53 μm (154 μm) ranges from 7% (3%) off nucleus to 0.5% (0.3%) near the nucleus. A simple interpretation of the observations of M82 invokes a massive polar outflow, dragging the field along, from a region ∼700 pc in diameter that has entrained some of the gas and dust, creating a vertical field geometry seen mostly in the hotter (53 μm) dust emission. This outflow sits within a larger disk with a more typical planar geometry that more strongly contributes to the cooler (154 μm) dust emission. For NGC 253, the polarization at 89 μm is dominated by a planar geometry in the tilted disk, with weak indication of a vertical geometry above and below the plane from the nucleus. The polarization observations of NGC 253 at 53 μm were of a insufficient signal-to-noise ratio for a detailed analysis.