  Here we show that for $k\in \mathbb N,$ the closure of the $k$-rank numerical
range of a contraction $A$ acting on an infinite-dimensional Hilbert space
$\mathcal{H}$ is the intersection of the closure of the $k$-rank numerical
ranges of all unitary dilations of $A$ to $\mathcal{H}\oplus\mathcal{H}.$ The
same is true for $k=\infty$ provided the $\infty$-rank numerical range of $A$
is non-empty. These generalize a finite dimensional result of Gau, Li and Wu.
We also show that when both defect numbers of a contraction are equal and
finite ($=N$), one may restrict the intersection to a smaller family consisting
of all unitary $N$-dilations. A result of {Bercovici and Timotin} on unitary
$N$-dilations is used to prove it. Finally, we have investigated the same
problem for the $C$-numerical range and obtained the answer in negative.
