  A paired dominating set $P$ is a dominating set with the additional property
that $P$ has a perfect matching. While the maximum cardainality of a minimal
dominating set in a graph $G$ is called the upper domination number of $G$,
denoted by $\Gamma(G)$, the maximum cardinality of a minimal paired dominating
set in $G$ is called the upper paired domination number of $G$, denoted by
$\Gamma_{pr}(G)$. We first show that $\Gamma_{pr}(G)\leq 2\Gamma(G)$ for any
graph $G$. We then focus on the graphs satisfying the equality $\Gamma_{pr}(G)=
2\Gamma(G)$. We give characterizations for two special graph classes: bipartite
and unicyclic graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ by using the results of
Ulatowski (2015). Besides, we study the graphs with $\Gamma_{pr}(G)=
2\Gamma(G)$ and a restricted girth. In this context, we provide two
characterizations: one for graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ and girth
at least 6 and the other for $C_3$-free cactus graphs with $\Gamma_{pr}(G)=
2\Gamma(G)$. We also pose the characterization of the general case of
$C_3$-free graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ as an open question.
