We report the three-dimensional electromagnetic simulation of gold nanoparticles with specific geometries as a means to the rational design of apertureless near-field scanning optical microscopy (NSOM) probes. Analytical solutions for field enhancement by spheroidal particles are used to provide physical insight for probe design. These solutions indicate that probes need to be not only sharp, but also finite in length in order to generate the highest field enhancement. Finite difference time domain (FDTD) simulations of gold particles illuminated by near infrared radiation are performed. Field enhancements for right trigonal pyramids are found to be size and wavelength dependent. Furthermore, the enhancements for these pyramidal particles are higher than for similar length conical particles, which in turn perform better than quasi-infinite conical probes. The particles we design with FDTD can be made using current nanofabrication techniques, and therefore hold great promise as apertureless NSOM probes. These right trigonal pyramids are particularly well suited for use in tip enhanced nonlinear optical microscopy or near-field Raman microscopy.