Pressure dependence of the upper critical field of MgB2 and of YNi2B2C

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.