Method and machine to manufacture a coil around a component of an article includes a main conveyor that moves along a working path and a carriage with a seat to house the component. Along the working path, the component is arranged in the seat of the carriage in an input station, and at a winding station, a wire having a diameter less than 500 μm is directly wound around the component for a winding time ranging from 50% to 70% of the total work cycle, to obtain the coil with a number of turns less than 50. A work cycle lasts from an initial instant, in which the carriage carrying the component without the coil reaches the winding station, to a final instant, in which the carriage carrying the component with the coil leaves the winding station.