Calculations of the electric-field enhancements in the vicinity of an illuminated silver tip, modeled using a Drude dielectric response, have been performed using the finite difference time domain method. Tip-induced field enhancements, of application in "apertureless" Raman scanning near-field optical microscopy (SNOM), result from the resonant excitation of plasmons on the metal tip. The sharpness of the plasmon resonance spectrum and the highly localized nature of these modes impose conditions to better exploit tip plasmons in tip-enhanced apertureless SNOM. The effect of tip-to-substrate separation and polarization on the resolution and enhancement are analyzed, with emphasis on the different field components parallel and perpendicular to the substrate.