The authors have measured the pressure dependence of the Knight shift and the linewidth of the nuclear magnetic resonance (NMR) signals of 7Li (up to 8 GPa) and 23Na (up to 6 GPa) in metallic lithium and sodium, respectively, at room temperature using a diamond anvil cell (DAC). It is concluded that diffusion is hindered by pressure; the diffusion coefficients and the activation volumes are estimated. In Li, diffusion increases at the BCC-FCC phase transition. The Li Knight shift increases with rising pressure up to the phase transition, where a marked reduction is observed which might be due to a drastic decrease of the s character of the conduction electron wave function. The Na shift decreases up to about 1.7 GPa and then increases. The Knight shift data are compared with theories that exist for pressures up to 1 GPa. By extrapolating existing values for the Pauli susceptibility, the pressure dependence of the spin density at the nuclear site is estimated.