  Every compact K\"ahler manifold with negative first Chern class admits a
unique metric $g$ such that $\text{Ric}(g) = -g$. Understanding how families of
these metrics degenerate gives insight into their geometry and is important for
understanding the compactification of the moduli space of negative
K\"ahler-Einstein metrics. I study a special class of such families in complex
dimension two. Following the work of Sun and Zhang (2019) in the Calabi-Yau
case, I construct a K\"ahler-Einstein neck region interpolating between
canonical metrics on components of the central fiber. This provides a model for
the limiting geometry of metrics in the family.
