Moving objects in the Z axis according to height of another object?

Hey guys, I have a terrain mesh (not using the in-built terrain system) with loads of blockout objects around and I keep moving the terrain around to see if there are more interesting shots I can do but the problem is, every time I do this, the blockout objects stay in the same place which are either floating, or cutting through the ground.

So… I was just wondering if there’s a way to ‘stick’ meshes to the terrain only in the Z axis? So that when I move the terrain, the objects will adjust their height accordingly and sit on the terrain.

Thanks in advance for any help!