Digital waveguide mesh (DWM) models are time-domain numerical methods providing computationally simple solutions for wave propagation problems. They have been used in various acoustical modeling and audio synthesis applications including synthesis of musical instrument sounds and speech, and modeling of room acoustics. A successful model of room acoustics should be able to account for source and receiver directivity. Methods for the simulation of directional sources in DWM models were previously proposed. This paper presents a method for the simulation of directional microphones in DWM-based models of room acoustics. The method is based on the directional weighting of the microphone response according to the instantaneous direction of incidence at a given point. The direction of incidence is obtained from instantaneous intensity that is calculated from local pressure values in the DWM model. The calculation of instantaneous intensity in DWM meshes and the directional accuracies of different mesh topologies are discussed. An intensity-based formulation for the response of a directional microphone is given. Simulation results for an actual microphone with frequency-dependent, non-ideal directivity function are presented.