We have imaged two normal, non-coronal, infrared-bright K giants, Alpha Tau and Alpha Boo, in the 1.4-mm and 2.8-mm continuum using the Berkeley Illinois Maryland Association millimeter array. These stars have been used as important absolute calibrators for several infrared infrared satellites. Our goals are: (1) to establish whether these stars radiate as simple photospheres or possess long-wavelength chromospheres; and (2) to make a connection between millimeter wave and far-infrared absolute flux calibrations. To accomplish these goals we also present Infrared Space Observatory Long Wavelength Spectrometer measurements of both these K giants. The far-infrared and millimeter continuum radiation is produced in the vicinity of the temperature minimum in Alpha Tau and Alpha Boo. We find that current photospheric models predict fluxes in reasonable agreement with those observed for wavelengths which sample the upper photosphere, namely <=125 microns in Alpha Tau and Alpha Boo. We clearly detect chromospheric radiation from both stars by 2.8mm (by 1.4mm in the case of Alpha Boo). Only additional observations can determine precisely where beyond 125 microns the purely radiative models fail. Until then, purely radiative models for these stars can only be used with confidence for calibration purposes below 125 microns.
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