We present the results of a submillimeter survey of 53 low-mass dense cores with the Submillimeter High Angular Resolution Camera II (SHARC-II). The survey is a follow-up project to the Spitzer Legacy Program ``From Molecular Cores to Planet-Forming Disks, with the purpose being to create a complete data set of nearby low-mass dense cores from the infrared to the millimeter. We present maps of 52 cores at 350 microns and three cores at 450 microns, two of which were observed at both wavelengths. Of these 52 cores, 41 were detected by SHARC-II: 32 contained one submillimeter source while 9 contained multiple sources. For each submillimeter source detected, we report various source properties including source position, fluxes in various apertures, size, aspect ratio, and position angle. For the 12 cores that were not detected we present upper limits. The sources detected by SHARC-II have, on average, smaller sizes at the 2sigma contours than those derived from longer-wavelength bolometer observations. We conclude that this is not caused by a failure to integrate long enough to detect the full extent of the core; instead it arises primarily from the fact that the observations presented in this survey are insensitive to smoothly varying extended emission. We find that SHARC-II observations of low-mass cores are much better suited to distinguishing between starless and protostellar cores than observations at longer wavelengths. Very Low Luminosity Objects, a new class of objects being discovered by the Spitzer Space Telescope in cores previously classified as starless, look very similar at 350 microns to other cores with more luminous protostars.
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