  We study the process of quantum tunnelling in scalar-tensor theories in which
the scalar field is non-minimally coupled to gravity. In these theories
gravitational instantons can deviate substantially from sphericity and can in
fact develop a neck - a feature prohibited in theories with minimal coupling.
Such instantons with necks lead to the materialisation of bubble geometries
containing a wormhole region. We clarify the relationship of neck geometries to
violations of the null energy condition, and also derive a bound on the size of
the neck relative to that of the instanton.
