  The residual closure of a subgroup $H$ of a group $G$ is the intersection of
all virtually normal subgroups of $G$ containing $H$. We show that if $G$ is
generated by finitely many cosets of $H$ and if $H$ is commensurated, then the
residual closure of $H$ in $G$ is virtually normal. This implies that separable
commensurated subgroups of finitely generated groups are virtually normal. A
stream of applications to separable subgroups, polycyclic groups, residually
finite groups, groups acting on trees, lattices in products of trees and
just-infinite groups then flows from this main result.
