The cap (1) has an annular cavity (4) formed between an outer cap region and an inner cap region. The annular cavity is formed for engagement of an annular connecting piece of a connector. The inner cap region comprises swabs (5) for cleaning and/or disinfecting a membrane of the connector reset to an edge of the connecting piece. The inner cap region includes a retaining projection (6) on which the swabs are fastened. The swabs extend over the retaining projection. The outer cap region and the inner cap region are connected with each other by a cap base (7). An independent claim is also included for a method for cleaning and/or disinfecting a surface of a membrane of a connector with a protective cap.