A bottle centering device for a capping machine for caps made of compressible material includes a support structure, associated with a compression box at a cap compression seat and defining an opening for passing a compressed cap and a cap insertion punch. The support structure is mountable on the compression box so that the through opening has a central axis axially centered on the cap compression seat. A bottle centerer defining an invitation seat and a central through opening is configured for engagement by a bottle mouth and is shaped to guide the mouth towards the through opening axially aligning with the central axis. The bottle centerer includes pieces angularly distributed about the central axis and each partially defining a portion of the invitation seat. The pieces are radially movable with respect to the central axis to vary radial dimensions of the invitation seat and the central through opening.