Measures of galaxy dust and gas mass with Herschel photometry and prospects for ALMA

(Abridged) Combining the deepest Herschel extragalactic surveys (PEP, GOODS-H, HerMES), and Monte Carlo mock catalogs, we explore the robustness of dust mass estimates based on modeling of broad band spectral energy distributions (SEDs) with two popular approaches: Draine & Li (2007, DL07) and a modified black body (MBB). As long as the observed SED extends to at least 160-200 micron in the rest frame, M(dust) can be recovered with a >3 sigma significance and without the occurrence of systematics. An average offset of a factor ~1.5 exists between DL07- and MBB-based dust masses, based on consistent dust properties. At the depth of the deepest Herschel surveys (in the GOODS-S field) it is possible to retrieve dust masses with a S/N>=3 for galaxies on the main sequence of star formation (MS) down to M(stars)~1e10 [M(sun)] up to z~1. At higher redshift (z<=2) the same result is achieved only for objects at the tip of the MS or lying above it. Molecular gas masses, obtained converting M(dust) through the metallicity-dependent gas-to-dust ratio delta(GDR), are consistent with those based on the scaling of depletion time, and on CO spectroscopy. Focusing on CO-detected galaxies at z>1, the delta(GDR) dependence on metallicity is consistent with the local relation. We combine far-IR Herschel data and sub-mm ALMA expected fluxes to study the advantages of a full SED coverage.