It depends a bit on how your animation system works, but what works well for static boxes is to just take the bounds of the mesh, and get maximum of width/height/depth and size the box in all dimensions with that amount. So the same as mentioned above but without using any keyframes.
Some methods of calculating bounds that I implemented:
1.) Contain all node/bone global positions
2.) Contain all (skinned) vertex positions
3.) Contain all OBB's of each node/bone
4.) Static box that moves with the position of the actor (method as described above)
The method using keyframes would only work if you do not blend or combine motions or do not do any procedural things. Or you would have to pass your full motion database through it. But this is quite overkill. Also if you choose to go with this method, you most likely will sample your animation curves when importing them from the software you exported with. For example if you load an FBX or use an exporter from Max or Maya you sample the transforms every n frames and possibly optimize that data. This means that it is highly unlikely that you would hit a case where you export just 2 keyframes for a 360 degree rotation.