Various devices and technologies using nanowires and nanoparticles are under intense investigation because of their promise. In these devices, nanowires or nanoparticles are typically in contact with another surface. The contact between a nanowire and a nanoparticle with a substrate forms a constriction of the order of a few nanometers. A continuum description of heat transport at these nanosized constrictions will break down. In this paper, an analytical model is presented in which the relevant length scales have been taken into consideration. The results show that the constriction resistance of nanoconstrictions is much higher than those predicted using macroscopic approaches. The Knudsen number is the key parameter for constriction formed between the same materials, whereas the microscopic Biot number based on phonon thermal boundary resistance is the key parameter for constriction formed between dissimilar materials. Finally, the model is applied to calculate the thermal resistance of the nanowire/planar interface.