Yes, they tend to be strict with the age limits for the ship booked tours. But as LisaP says, try a independant tour guide (look on the internet). If you come back here with which port you are planning to do this in and what it is you want to do, you can get recommendations on no ship based tour companies. They will tend to let younger kids go on the tours. Just ask when you call to book them.
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, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013