  We consider harmonic diffeomorphisms to a fixed hyperbolic target $Y$, from a
family of domain Riemann surfaces degenerating along a Teichm\"{u}ller ray. We
use the work of Minsky to show that there is a limiting harmonic map from the
conformal limit of the Teichm\"{u}ller ray, to a crowned hyperbolic surface.
The target surface is the metric completion of the complement of a geodesic
lamination on $Y$. The conformal limit is obtained by attaching half-planes and
cylinders to the critical graph of the holomorphic quadratic differential
determining the ray. As an application, we provide a new proof of the existence
of harmonic maps from any punctured Riemann surface to a given crowned
hyperbolic target of the same topological type.
