This paper responds to the expanding interest in archaeology in the use of portable X-Ray fluorescence (pXRF) technologies. Accurate analysis using pXRF requires correction for absorbance and secondary enhancement of the excited element X-rays by the other elements present. Several correction methods are widely used, including fundamental parameters, influence coefficients, Compton ratioing, multi-variate statistical analysis, and dilution. Most pXRF calibrations use either fundamental parameters or multi-variate statistics. However, influence coefficients are known to be the most certain calibration method for XRF analysis of geological materials. Portable XRF calibrations using influence coefficients in the analysis of obsidian, flint, mudbrick, and sediment have far less bias and include a wider range of elements (Mg through Ce) than multi-variate statistical or fundamental parameter calibrations using beam filtered spectra. Bias v. wavelength dispersive XRF data using influence coefficients is mostly less than 1 % for obsidian and flint, and less than 2 % for mudbrick and sediment, in contrast with the large biases (up to 36 %) found using fundamental parameters or multi-variate statistical methods.