A few ideas that haven't been tossed around:
1) Once loaded, the airship and everything on it is turned into gaseous form.
2) Once loaded, the airship and everything on it is made incorporeal.
3) The airship isn't floating -- it's teleporting very short distances (inches, if that) several times per second, so that anyone on deck feels a constant tremble from the ship doing these little lurches and beginning to fall and then getting teleported back up a few inches into the air. (All fear the the Dimensional Anchor spell!)
4) The airship hovers by the power of a constant-application of a specially tailored "Repel" type spell (like Repel Metal, Repel Life, etc) that is cast every round, and can be tailored for different distances to control altitude. This means that ships cannot go under each other without catastrophic consequences, and ship battles involve trying to maneuver above your opponent so that your own repulsion field slams into that ship, causing it to fly up and hit your very well-protected hull, which likely kills anyone on the top deck of the victim ship and definitely wreaks havoc with the sails and mast.
5) The ship uses a combination of magically created matter (think Decanter of Endless Water) and matter destruction (think Sphere of Annihilation) to generate vast amounts of force. If the drive hold has ten decanters set into the hull and firing water at full force, with a Sphere of Annihilation to catch and remove the water, the ship is lifted into the air by the force of the decanters.