Properties of the field electron emission for diamond/pyrocarbon nanocomposites produced from diamond particles surrounded by an sp(2)-bonded pyrocarbon matrix are considered as functions of a size of diamond particles selected in the range of 5 nm - 5 mum, and of an average thickness of the pyrocarbon shell controlled by the pyrocarbon/diamond mass ratio varied from 0 to 0.5. The low-threshold emission at fields of greater than or equal to1 V/mum with ''no activation/no hysteresis'' I-V behavior was observed for these materials using tungsten tip microprobes as well as a fluorescent screen. A specially designed scanning tunneling-field emission microscope was used for simultaneous mapping of field emission intensity, topography, work function, and electrical resistivity to study the mechanisms of the emission from the composites and well-emitting chemical vapor deposition diamond films. It was found that for both of the materials emission centers are associated with interfaces between diamond and sp2-bonded carbon phases. Possible mechanisms of the low-field electron emission for the diamond/graphite composites including local field enhancement are analyzed. A model of the low-field emission based on quantum well effect at the diamond/graphite interface is proposed and discussed.