A machine for conveying containers, comprising: a guide extending along an advancement direction of the containers; a main carriage slidably mounted on said guide, said guide and said main carriage together defining a main linear motor; at least one auxiliary carriage slidably mounted on said guide, said guide and said auxiliary carriage together defining an auxiliary linear motor; a pressing device mounted on said main carriage and movable along an axis coinciding with the main axis of the container between a raised rest position, in which the pressing device and the container are not in contact, and a lowered constrained position in which the pressing device applies a pressing force on the top of a container; a control unit electrically connected to said guide and configured for controlling the sliding of said main carriage and said auxiliary carriage on said guide and a mutual distance thereof; actuating means operatively connected to said pressing device and configured for moving said pressing device between said raised rest position and said lowered constrained position; said actuating means being operatively interposed between said pressing device and said auxiliary carriage, and being activatable following the variation of the mutual distance between said main carriage and said auxiliary carriage; said control unit being configured for commanding the variation of the mutual distance between the main carriage and the auxiliary carriage so as to activate said actuating means; wherein the pressing device is rotationally independent of the axial movement between the raised rest position and the lowered constrained position. a guide extending along an advancement direction of the containers; a main carriage slidably mounted on said guide, said guide and said main carriage together defining a main linear motor; at least one auxiliary carriage slidably mounted on said guide, said guide and said auxiliary carriage together defining an auxiliary linear motor; a pressing device mounted on said main carriage and movable along an axis coinciding with the main axis of the container between a raised rest position, in which the pressing device and the container are not in contact, and a lowered constrained position in which the pressing device applies a pressing force on the top of a container; a control unit electrically connected to said guide and configured for controlling the sliding of said main carriage and said auxiliary carriage on said guide and a mutual distance thereof; actuating means operatively connected to said pressing device and configured for moving said pressing device between said raised rest position and said lowered constrained position; said actuating means being operatively interposed between said pressing device and said auxiliary carriage, and being activatable following the variation of the mutual distance between said main carriage and said auxiliary carriage; said control unit being configured for commanding the variation of the mutual distance between the main carriage and the auxiliary carriage so as to activate said actuating means; wherein the pressing device is rotationally independent of the axial movement between the raised rest position and the lowered constrained position.