We present an integral field spectroscopic study of two nearby luminous infrared galaxies (LIRGs), IC 1623 and NGC 3256, which exhibit evidence of widespread shock excitation induced by ongoing merger activity. We show the importance of carefully separating excitation due to shocks versus excitation by H II regions and the usefulness of integral field unit data in interpreting the complex processes in LIRGs. Our analysis focuses primarily on the emission line gas, which is extensive in both systems and is a result of the abundant ongoing star formation as well as widespread LINER-like excitation from shocks. We use emission line ratio maps, line kinematics, line-ratio diagnostics, and new models as methods for distinguishing and analyzing shocked gas in these systems. We discuss how our results inform the merger sequence associated with local U/LIRGs and the impact that widespread shock excitation has on the interpretation of emission line spectra and derived quantities of both local and high-redshift galaxies.