  Let $R$ be a commutative ring, and let $S$ be a multiplicative subset of $R$.
In this paper, we investigate the notion of $S$-cotorsion modules. An
$R$-module $C$ is called $S$-cotorsion if $\text{Ext}^{1}_{R}(F,C) = 0$ for
every $S$-flat $R$-module $F$. Among other results, we establish that the pair
$(S\mathcal{F}, S\mathcal{C})$, where $S\mathcal{F}$ denotes the class of all
$S$-flat $R$-modules and $S\mathcal{C}$ denotes the class of all $S$-cotorsion
modules, forms a hereditary perfect cotorsion pair. As applications, we provide
characterizations of $S$-perfect rings in terms of $S$-cotorsion modules. We
conclude the paper with results on $S\mathcal{F}$-preenvelopes. Namely, we
prove that if every module has an $S\mathcal{F}$-preenvelope, then $R$ is
$S$-coherent. Furthermore, we establish the converse under the condition that
$R_S$ is a finitely presented $R$-module.
