No cruise line charges for the tenders when in a tender port (i.e. no docking capacity for the ship).
And there really is no limit on the number of trips to and from teh ship you make. Just make sure you are back on board before the ship sails.
Ideally you would like to avoid the hassle of tendering and go to port where you can dock. This makes the whole proceedure go faster. On tender ports, they will let those with early excursions off the ship first and there is generally a line to get onto the tenders.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013