  We report magnetotransport measurements of the critical field behavior of
thin Al films deposited onto multiply connected substrates. The substrates were
fabricated via a standard electrochemical process that produced a triangular
array of 66 nm diameter holes having a lattice constant of 100 nm. The critical
field transition of the Al films was measured near $T_c$ as a function of field
orientation relative to the substrate normal. With the field oriented along the
normal ($\theta=0$), we observe reentrant superconductivity at a characteristic
matching field $H_m=0.22\,\mathrm{T}$, corresponding to one flux quantum per
hole. In tilted fields, the position $H^*$ of the reentrance feature increases
as $\sec(\theta)$, but the resistivity traces are somewhat more complex than
those of a continuous superconducting film. We show that when the tilt angle is
tuned such that $H^*$ is of the order of the upper critical field $H_c$, the
entire critical region is dominated by the enhanced dissipation associated with
a sub-matching perpendicular component of the applied field. At higher tilt
angles a local maximum in the critical field is observed when the perpendicular
component of the field is equal to the matching field.
