  Conformally St{\"a}ckel manifolds can be characterized as the class of
n-dimensional pseudo-Riemannian manifolds (M, G) on which the Hamilton-Jacobi
equation G($\nabla$u, $\nabla$u) = 0 for null geodesics and the Laplace
equation --$\Delta$ G $\psi$ = 0 are solvable by R-separation of variables. In
the particular case in which the metric has Riemannian signature, they provide
explicit examples of metrics admitting a set of n--1 commuting conformal
symmetry operators for the Laplace-Beltrami operator $\Delta$ G. In this paper,
we solve the anisotropic Calder{\'o}n problem on compact 3-dimensional
Riemannian manifolds with boundary which are conformally St{\"a}ckel, that is
we show that the metric of such manifolds is uniquely determined by the
Dirichlet-to-Neumann map measured on the boundary of the manifold, up to
dieomorphims that preserve the boundary.
