  In this paper, the classical and quantum solutions of some axisymmetric
cosmologies coupled to a massless scalar field are studied in the context of
minisuperspace approximation. In these models, the singular nature of the
Lagrangians entails a search for possible conditional symmetries. These have
been proven to be the simultaneous conformal symmetries of the supermetric and
the superpotential. The quantization is performed by adopting the Dirac
proposal for constrained systems, i.e. promoting the first-class constraints to
operators annihilating the wave function. To further enrich the approach, we
follow \cite{Christodoulakis:2012eg} and impose the operators related to the
classical conditional symmetries on the wave function. These additional
equations select particular solutions of the Wheeler-DeWitt equation. In order
to gain some physical insight from the quantization of these cosmological
systems, we perform a semiclassical analysis following the Bohmian approach to
quantum theory. The generic result is that, in all but one model, one can find
appropriate ranges of the parameters, so that the emerging semiclassical
geometries are non-singular. An attempt for physical interpretation involves
the study of the effective energy-momentum tensor which corresponds to an
imperfect fluid.
