  We extend Culler and Shalen's construction of detecting essential surfaces in
3-manifolds to 3-orbifolds. We do so in the setting of the
$\mathrm{SL}_2(\mathbb{C})$ character variety, and following Boyer and Zhang in
the $\mathrm{PSL}_2(\mathbb{C})$ character variety as well. We show that any
slope detected on a canonical component of the $\mathrm{(P)SL}_2(\mathbb{C})$
character variety of a one cusped hyperbolic 3-manifold with symmetries must be
the slope of a symmetric surface. As an application, we show that for each
symmetric double twist knot there are slopes which are strongly detected on the
character variety but not on the canonical component.
