  For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined
Cambrian semilattices $C_{\gamma}$ as semilattice quotients of the weak order
on $W$ induced by certain semilattice homomorphisms. In this article, we define
an edge-labeling using the realization of Cambrian semilattices in terms of
$\gamma$-sortable elements, and show that this is an EL-labeling for every
closed interval of $C_{\gamma}$. In addition, we use our labeling to show that
every finite open interval in a Cambrian semilattice is either contractible or
spherical, and we characterize the spherical intervals, generalizing a result
by Nathan Reading.
