We provide a canonical construction of conformal covers for finite
hypergraphs and present two immediate applications to the finite model
theory of relational structures. In the setting of relational
structures, conformal covers serve to construct guarded bisimilar
companion structures that avoid all incidental Gaifman cliques—thus
serving as a partial analogue in finite model theory for the usually
infinite guarded unravellings. In hypergraph theoretic terms, we show
that every finite hypergraph admits a bisimilar cover by a finite
conformal hypergraph. In terms of relational structures, we show that
every finite relational structure admits a guarded bisimilar cover by
a finite structure whose Gaifman cliques are guarded. One of our
applications answers an open question about a clique constrained
strengthening of the extension property for partial automorphisms
(EPPA) of Hrushovski, Herwig and Lascar. A second application
provides an alternative proof of the finite model property (FMP) for
the clique guarded fragment of first-order logic CGF, by reducing
(finite) satisfiability in CGF to (finite) satisfiability in the
guarded fragment, GF.