Results of observations of NGC 4945 and the Circinus galaxy carried out with a 1 m balloon-borne far-infrared telescope are reported. While only an upper limit (5-sigma) of 150 Jy for the 150-mu-m flux density is obtained for Circinus, the central region of NGC 4945 has been mapped in two bands with effective wavelengths of approximately 58 and approximately 150-mu-m. Pointed observations of IRAS, using survey detectors, have been deconvolved to get higher angular resolution intensity maps at 12, 25, 60, and 100-mu-m, respectively, for both of these galaxies. In addition, using the maps in the neighboring bands (12/25, 25/60, and 60/100), spatial distributions of the dust temperature and the optical depth have also been obtained. In NGC 4945, the nucleus has been found to be cooler than its immediate surroundings. Deconvolved intensity maps have also been obtained from the IRAS Chopped Photometric Channel data at 50 and 100-mu-m. Whereas both these galaxies show a prominent central source, only NGC 4945 shows extended disk emission in all bands. The central source in both the galaxies is found to be somewhat more extended than a point source at wavelengths 50-mu-m or greater, the resulting deconvolved size being approximately 40". Symmetric spiral arm like features of NGC 4945 seen in the far-infrared IRAS maps have counterparts in radio continuum, H I and (CO)-C-12 maps. The 150-mu-m observations for NGC 4945, for epsilon-is-proportional-to-lambda-1 indicate presence of dust cooler than that implied by the IRAS observations. The 150-mu-m upper limit for the Circinus galaxy implies a steeper wavelength dependence of dust emissivity (epsilon-is-proportional-to-lambda-2 or steeper) than is the case for NGC 4945.