We investigate electronic transport through molecular radicals and predict a correlation-induced transmission node arising from destructive interference between transport contributions from different charge states of the molecule. This quantum interference effect has no single-particle analog and cannot be described by effective single-particle theories. Large errors in the thermoelectric properties and nonlinear current-voltage response of molecular radical junctions are introduced when the complementary wave and particle aspects of the electron are not properly treated. A method to accurately calculate the low-energy transport through a radical-based junction using an Anderson model is given.