We present 321 GHz observations of five active galactic nuclei (AGNs) from ALMA Cycle 0 archival data: NGC 5793, NGC 1068, NGC 1386, NGC 4945, and the Circinus galaxy. Submillimeter maser emission is detected for the first time toward NGC 4945, and we present a new analysis of the submillimeter maser system in Circinus. None of the other three galaxies show maser emission, although we have detected and imaged the continuum from every galaxy. Both NGC 4945 and Circinus are known to host strong (10 Jy) 22 GHz megamaser emission, and VLBI observations have shown that the masers reside in the innermost ∼1 pc of the galaxies. The peak flux densities of the 321 GHz masers in both systems are substantially weaker (by a factor of ∼100) than what is observed at 22 GHz, although the corresponding isotropic luminosities are more closely matched (within a factor of ∼10) between the two transitions. We compare the submillimeter spectra presented here to the known 22 GHz spectra in both galaxies, and we argue that while both transitions originate from the gaseous environment near the AGNs, not all sites are in common. In Circinus, the spectral structure of the 321 GHz masers indicates that they may trace the accretion disk at radii interior to the 22 GHz masers. The continuum emission in NGC 4945 and NGC 5793 shows a spatial distribution indicative of an origin in the galactic disks (likely thermal dust emission), while for the other three galaxies the emission is centrally concentrated and likely originates from the nucleus.