Let $R$ be a commutative ring with identity $1\neq 0$. In this paper, we continue the study started in [10] concerning when the extended zero-divisor graph of $R$, $\overlineΓ(R)$, is complemented. We also study when $\overlineΓ(R)$ is uniquely complemented. We give a complete characterization of when $\overlineΓ(R)$ of a finite ring is complemented. Various examples are given using the direct product of rings and idealizations of modules.