  We present measurements of H$_{c2}(T)$ under pressure in MgB$_2$ and in
YNi$_2$B$_2$C. The changes in the shape of H$_{c2}(T)$ are interpreted within
current models and show the evolution of the main Fermi surface velocities
$v_F$ and electron-phonon coupling parameters $\lambda$ with pressure. In
MgB$_2$ the electron-phonon coupling strength of the nearly two dimensional
$\sigma$ band, responsible for the high critical temperature, is more affected
by pressure than the $\pi$ band coupling, and the hole doping of the $\sigma$
band decreases. In YNi$_2$B$_2$C, the peculiar positive curvature of
H$_{c2}(T)$ is weakened by pressure.
