Water depth in the Rove tunnel is 4m, and 12m in the Stad tunnel. They don't say at what state of the tide that is though, which I would have thought affects the size of ship that can pass through significantly (unless it has locks either end I suppose).

From Wikipedia:

Rove:

    Length - 7,120 metres (23,360 ft) long
    Clearance - 15 m (49 ft)
    Width - 22 m (72 ft)

    Length - 1800 metres
    Clearance - 49 metres
    Width - 37 metres
    Boat-passable - 16 metres
    Depth of tunnel below water level - 12 metres