  A matching $M$ in a graph $G$ is uniquely restricted if no other matching in
$G$ covers the same set of vertices. We conjecture that every connected
subcubic graph with $m$ edges and $b$ bridges that is distinct from $K_{3,3}$
has a uniquely restricted matching of size at least $\frac{m+b}{6}$, and we
establish this bound with $b$ replaced by the number of bridges that lie on a
path between two vertices of degree at most $2$. Moreover, we prove that every
connected subcubic graph of order $n$ and girth at least $7$ has a uniquely
restricted matching of size at least $\frac{n-1}{3}$, which partially confirms
a Conjecture of F\"{u}rst and Rautenbach (Some bounds on the uniquely
restricted matching number, arXiv:1803.11032).
