Is it condensation or a roof leak. I will assume condensation which is caused by warm moist air contacting a cold surface. The fix is to have less moist air (turn off humidifier or fix/use bathroom vents when having a shower) OR improve the insulating value of the sun tunnel. I have no personal experience with the sun tunnel but is the glass dome double glazed? If not, and it's cold there is no way that you can stop condensation as the glass surface will be cold. The only thing you could do is manage the condensation flow using a gutter system. Not good.

Good luck. Anyone familar with the Velux and whether they are double or triple glazed?

Sounds to me like it is leaking around the tunnel itself. Perhaps through the ridgevent and running down around the tunnel? Velux is only responsible if it is seal failure around or between the glass. That doesn't sound like the case here.

Thanks for the replies. The rooms in question are a powder room (seldom used) and a utility room, and in both cases both rooms have little moisture as they're off a well-used hallway with lots of air flow. In the winter, there's usually general condensation inside the Velux dome, so it looks brilliant white against our dark shingles. I wasn't sure if that was supposed to happen or not. The current situation is definitely a leak though. I collected a quart or two of water, plus the moisture that damaged the ceiling. I didn't think it would do me any good to have my regular contractor come out to fix it because he doesn't know what to do- he thought he installed it correctly per instructions. If the problem isn't covered under warranty, Velux said they would charge $85. My thought was I might as well have Velux come tell me if it's a warranty problem or pay them to fix it right rather than paying my local guy to do a trial & error. But I'm wondering if Velux will ever even show since it's already been 2 1/2 weeks since I contacted them and I'm still waiting.

I would stay away from velux products they will not honor there warrentys I have a $475 skylight installed in 05 it starting leaking 6 months after the install it has been proved it isnt the installation to roof leaking but the seal on the sash the company doesnt care customer service is far from the companys core value of doing business. My advise is to look for another company line of products. I wish you well.
Tim