  We use virtual knot theory to detect the non-invertibility of some classical
links in $\mathbb{S}^3$. These links appear in the study of virtual covers.
Briefly, a virtual cover associates a virtual knot $\upsilon$ to a knot $K$ in
a $3$-manifold $N$, under certain hypotheses on $K$ and $N$. Virtual covers of
links in $\mathbb{S}^3$ come from taking $K$ to be in the complement $N$ of a
fibered link $J$. If $J \sqcup K$ is invertible and $K$ is "close to" a fiber
of $J$, then $\upsilon$ satisfies a symmetry condition to which some virtual
knot polynomials are sensitive. We also discuss virtual covers of links $J
\sqcup K$ where $J$ is not fibered but is virtually fibered (in the sense of W.
Thurston).
