The James Webb Space Telescope (JWST), as the largest space-based astronomical observatory with near- and mid-infrared instrumentation, will elucidate many mysterious aspects of comets. We summarize four cometary science themes especially suited for this telescope and its instrumentation: the drivers of cometary activity, comet nucleus heterogeneity, water ice in comae and on surfaces, and activity in faint comets and main-belt asteroids. With JWST, we can expect the most distant detections of gas, especially CO2, in what we now consider to be only moderately bright comets. For nearby comets, coma dust properties can be studied with their driving gases, measured simultaneously with the same instrument or contemporaneously with another. Studies of water ice and gas in the distant Solar System will help us test our understanding of cometary interiors and coma evolution. The question of cometary activity in main-belt comets will be further explored with the possibility of a direct detection of coma gas. We explore the technical approaches to these science cases and provide simple tools for estimating comet dust and gas brightness. Finally, we consider the effects of the observatorys non-sidereal tracking limits, and provide a list of potential comet targets during the first 5 years of the mission.