  One presents a phase-space noncommutative extension of Quantum Cosmology in
the context of a Kantowski-Sachs (KS) minisuperspace model. We obtain the
Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM
formalism and a suitable Seiberg-Witten map. The resulting WDW equation
explicitly depends on the phase-space noncommutative parameters, $\theta$ and
$\eta$. Numerical solutions of the noncommutative WDW equation are found and,
interestingly, also bounds on the values of the noncommutative parameters.
Moreover, we conclude that the noncommutativity in the momenta sector leads to
a damped wave function implying that this type of noncommutativity can be
relevant for a selection of possible initial states for the universe.
