  The catenary degree is an invariant that measures the distance between
factorizations of elements within an atomic monoid. In this paper, we classify
which finite subsets of $\mathbb Z_{\ge 0}$ occur as the set of catenary
degrees of a numerical monoid (i.e., a co-finite, additive submonoid of
$\mathbb Z_{\ge 0}$). In particular, we show that, with one exception, every
finite subset of $\mathbb Z_{\ge 0}$ that can possibly occur as the set of
catenary degrees of some atomic monoid is actually achieved by a numerical
monoid.
