  Inertial magnetization dynamics have been predicted at ultrahigh speeds, or
frequencies approaching the energy relaxation scale of electrons, in
ferromagnetic metals. Here we identify inertial terms to magnetization dynamics
in thin Ni$_{79}$Fe$_{21}$ and Co films near room temperature. Effective
magnetic fields measured in high-frequency ferromagnetic resonance (115-345
GHz) show an additional stiffening term which is quadratic in frequency and
$\sim$ 80 mT at the high frequency limit of our experiment. Our results extend
understanding of magnetization dynamics at sub-picosecond time scales.
