  (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.
