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We study quadratic Lie conformal superalgebras associated with No\-vikovsuperalgebras. For every Novikov superalgebra $(V,\circ)$, we construct anenveloping differential Poisson superalgebra $U(V)$ with a derivation $d$ suchthat $u\circ v = ud(v)$ 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 superalgebraof $V$ is special. Next, we prove that every quadratic Lie conformalsuperalgebra constructed on a finite-dimensional special Gel'fand--Dorfmansuperalgebra has a finite faithful conformal representation. This statement isa step toward a solution of the following open problem: whether a finite Lieconformal (super)algebra has a finite faithful conformal representation.

Quadratic Lie conformal superalgebras related to Novikov superalgebras