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I have been on a lot of cruises, mediterrean,caribbean and alaska where there have been tenders and they have all been free, I have never heard about any paymen.
Normally tenders are free however in Venice in particular we have encountered a charge for tender tickets to go from the dock area to the mooring near St Mark's square. As I recall one small payment covered unlimited travel over the 2 to 3 days the ship was moored there and was well worth i.
Most tender journeys are fre.
There are no tender charges on RCI.. There may be a charge to get you by coach/bus from the ship to the nearest town though [like in Livorno or Civitavecchia.