We present first efforts to establish a network of absolutely calibrated continuous infrared spectra of standard stars across the 1-35μm range in order to calibrate arbitrary broad and narrow passbands and low-resolution spectrometers from ground-based, airborne, balloon, and satellite-borne sensors. The value to photometry of such calibrated continuous spectra is that one can integrate arbitrary filters over the spectra and derive the stellar in-band flux, monochromatic flux density, and hence the magnitude, for any site. This work is based on new models of Sirius and Vega by Kurucz which were calculated by him, for the first time, with realistic stellar metallicities and a customized finely-gridded infrared wavelength scale. We have absolutely calibrated these two spectra and have calculated monochromatic flux densities for both stars, and isophotal wavelengths, for a number of infrared filters. Preliminarily, the current IRAS point source flux calibration is too high by 2, 6, 3, and 12% at 12, 25, 60, and 100μm, respectively.