The pressure dependence of the Knight shift K of Al and Nb metals was measured with a digitally slaved signal averager. The maximum hydrostatic pressure utilized was 8000 kg/cm2. The observed value of dlnKdlnV is - 1.01+/-0.02 and - 0.29+/-0.02 for Al and Nb, respectively. Since it is essential to know the volume dependence of the (electron-electron-enhanced) spin susceptibility dlnχ*spdlnV in order to analyze the observed dlnKdlnV, the theoretical implication of the previously proposed methods to estimate dlnχ*spdlnV was explored. The linearly temperature-dependent thermal expansion at low temperature αe gives rise to the volume dependence of electron-phonon-enhanced density of states at the Fermi surface. αe includes only a temperature-independent part of the enhancement factor 1+λ. The pressure dependence of the superconductor parameters renders the volume dependence of the density of the states clothed with a full electron-phonon interaction, which includes the temperature-independent part as well as a possible temperature-dependent part. A semiempirical scheme to deduce the volume dependence of 1+λ, the density of states for the bare electrons N(EF)BS, and the band-structure effective mass m* is proposed. These values are derived from the pressure dependence of the superconducting transition temperature and αe. The volume dependence of χ*sp is deduced from dlnN(EF)BSdlnV by taking into account the effect of the electron-electron enhancement factor. The volume dependence of the density of wave function at the Fermi surface <|ψ(0)|2> was deduced for Al as dln<|ψ(0)|2>dlnV=-2.12. The volume dependence of the orbital Knight shift K0 for Nb is estimated as dlnK0dlnV~=0.4 (or 0.1). The possible origin of the discrepancy between the density of states derived from αe and from the pressure dependence of the superconductor parameters is discussed. The origin of inconsistency in the previously reported temperature dependence of K for Al is also suggested.