  We study eigenvalue problems for intrinsic sub-Laplacians on regular
sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues
$\lambda_k$ of conformal sub-Riemannian metrics that are asymptotically sharp
as $k\to +\infty$. For Sasakian manifolds with a lower Ricci curvature bound,
and more generally, for contact metric manifolds conformal to such Sasakian
manifolds, we obtain eigenvalue inequalities that can be viewed as versions of
the classical results by Korevaar and Buser in Riemannian geometry.
