  Precise measurements of SM particles properties at the LHC allows to look for
heavy New Physics in the context of an Effective Field Theory (EFT). These
searches, however, often rely on kinematic regions where the validity of the
EFT may be compromised. In this paper we propose to address this issue by
comparing with benchmark models. The connection between models and their
manifestations as EFTs at low energies allows us to quantify the breakdown of
the EFT, and describe ways to combine different sources of constraints beyond
Higgs physics. To illustrate these techniques, in this paper we propose a set
of benchmark models based on extensions of the Higgs sector, namely the
inclusion of a singlet, a dilaton and generic 2HDMs. We obtain the matching
between these models and the EFT involving the Higgs, electroweak bosons and
fermions. We then describe current and future indirect and direct constraints,
consider the effect of correlations among the coefficients within models, and
discuss the validity of the EFT.
