We characterize the dust in NGC628 and NGC6946, two nearby spiral galaxies in the KINGFISH sample. With data from 3.6um to 500um, dust models are strongly constrained. Using the Draine & Li (2007) dust model, (amorphous silicate and carbonaceous grains), for each pixel in each galaxy we estimate (1) dust mass surface density, (2) dust mass fraction contributed by polycyclic aromatic hydrocarbons (PAH)s, (3) distribution of starlight intensities heating the dust, (4) total infrared (IR) luminosity emitted by the dust, and (5) IR luminosity originating in regions with high starlight intensity. We obtain maps for the dust properties, which trace the spiral structure of the galaxies. The dust models successfully reproduce the observed global and resolved spectral energy distributions (SEDs). The overall dust/H mass ratio is estimated to be 0.0082+/-0.0017 for NGC628, and 0.0063+/-0.0009 for NGC6946, consistent with what is expected for galaxies of near-solar metallicity. Our derived dust masses are larger (by up to a factor 3) than estimates based on single-temperature modified blackbody fits. We show that the SED fits are significantly improved if the starlight intensity distribution includes a (single intensity) delta function component. We find no evidence for significant masses of cold dust T<12K. Discrepancies between PACS and MIPS photometry in both low and high surface brightness areas result in large uncertainties when the modeling is done at PACS resolutions, in which case SPIRE, MIPS70 and MIPS160 data cannot be used. We recommend against attempting to model dust at the angular resolution of PACS.