This paper presents state-of-the-art spectral energy distributions (SEDs) of four Herbig Ae stars, based in part on new data in the mid and far-infrared and at millimeter wavelengths. The SEDs are discussed in the context of circumstellar disk models. We show that models of irradiated disks provide a good fit to the observations over the whole range of wavelengths. We offer a possible solution to the long-standing puzzle caused by the excess emission of Herbig Ae stars, where a large fraction of the stellar luminosity is re-radiated between ~1.25 and 7 micron, with a peak at about 3 micron. We suggest that this general behaviour can be caused by dust evaporation in disks where the gas component is optically thin to the stellar radiation, as expected if the accretion rate is very low. The creation of a puffed-up inner wall of optically thick dust at the dust sublimation radius can account for the near-infrared characteristics of the SEDs. It can also naturally explain the H and K band interferometric observations of AB Aur (Millan-Gabet et al. 2001), which reveal a ring of emission of radius ~0.3 AU. Finally, irradiated disk models can easily explain the observed intensity of the 10 micron silicate features and their variation from star to star. Based in part on observations obtained with ISO and with the IRAM Plateau de Bure Interferometer. ISO is an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, The Netherlands and the UK) and with the participation of ISAS and NASA. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).