  The main goal of this paper is devoted to N(k)-contact metric manifolds
admitting $\ast$-conformal Einstein soliton and also $\ast$-conformal gradient
Einstein soliton. In this settings the nature of the manifold, and the
potential vector field, potential function of solitons are characterized, and
conditions for the $\ast$-conformal Einstein soliton to be expanding, steady,
or shrinking are also given. Furthermore, the nature of the potential vector
field is evolved when the metric g of N(k)-contact metric manifold satisfies
$\ast$-conformal gradient Einstein soliton. Finally, an illustrative example of
a N(k)-contact metric manifold is discussed to verify our findings.
