  We study quadratic Lie conformal superalgebras associated with No\-vikov
superalgebras. For every Novikov superalgebra $(V,\circ)$, we construct an
enveloping differential Poisson superalgebra $U(V)$ with a derivation $d$ such
that $u\circ v = ud(v)$ and $\{u,v\} = u\circ v - (-1)^{|u||v|} v\circ u$ for
$u,v\in V$. The latter means that the commutator Gelfand--Dorfman superalgebra
of $V$ is special. Next, we prove that every quadratic Lie conformal
superalgebra constructed on a finite-dimensional special Gel'fand--Dorfman
superalgebra has a finite faithful conformal representation. This statement is
a step toward a solution of the following open problem: whether a finite Lie
conformal (super)algebra has a finite faithful conformal representation.
