  A conformal Lie group is a conformal manifold $(M,c)$ such that $M$ has a Lie
group structure and $c$ is the conformal structure defined by a left-invariant
metric $g$ on $M$. We study Weyl-Einstein structures on conformal solvable Lie
groups and on their compact quotients. In the compact case, we show that every
conformal solvmanifold carrying a Weyl-Einstein structure is Einstein. We also
show that there are no left-invariant Weyl-Einstein structures on non-abelian
nilpotent conformal Lie groups, and classify them on conformal solvable Lie
groups in the almost abelian case. Furthermore, we determine the precise list
(up to automorphisms) of left-invariant metrics on simply connected solvable
Lie groups of dimension 3 carrying left-invariant Weyl-Einstein structures.
