If you want to keep them working on getting through the ward for a while, you could build a layered ward instead of one with high numbers. Make the outer layer of the ward around 4-5 shifts, nothing fancy, easy to break through. Once it is broken (which can also happen by someone trying to force his way inside), the real wards spring up. The next layer is still nothing too fancy, maybe 2 shifts better, but it will activate another level, and by then the wards specialist should realize, that this is not the way to go about it. He has to sever the connection between the layers, so the next layers won't be activated, when he breaks down the active wall. Ward 3 and above should have some nasty things built in, just to get the message across, that every layer will be worse than the last. I would let the wards specialist take down different aspects of a layer individually, as long as he was able to make them out through a lore roll. Sort of like the wizards equivalent to hacking, I suppose.
The concept should be especially fitting, if the BBG is on the sneaky side of bad, because you don't know how many layers you'll get, what the actual strength of the fortifications are. The next layer could be the last, or it could activate another ward while firing a bolt of lightning at you.
It is more of a mind game than just brute forcing your way through, and I think a wards specialist might enjoy something like this more than just hulk smashing through a magical brick wall.