  Multi-centered bubbling solutions are black hole microstate geometries that
arise as smooth solutions of 5-dimensional $\mathcal{N}=2$ Supergravity. When
these solutions reach the scaling limit, their resulting geometries develop an
infinitely deep throat and look arbitrarily close to a black hole geometry. We
depict a connection between the scaling limit in the moduli space of Microstate
Geometries and the Swampland Distance Conjecture. The naive extension of the
Distance Conjecture implies that the distance in moduli space between a
reference point and a point approaching the scaling limit is set by the proper
length of the throat as it approaches the scaling limit. Independently, we also
compute a distance in the moduli space of 3-centre solutions, from the K\"ahler
structure of its phase space using quiver quantum mechanics. We show that the
two computations of the distance in moduli space do not agree and comment on
the physical implications of this mismatch.
