The rounds for my .338 Edge are just shy of 4 inches and so far I havent been able to find a ammunition carrier/box that will accomidate a round that long. About all I have been able to find locally are the MTM flip top boxes which aren't quite tall enough. Looking for something that holds 20 to 50 rounds.
Check out the ammo vault thru midway. They will hold 20 rounds and have a padded top, they also are self locking. I use them for 300wm and 7rm. they seem to close about 3/4 of the way with those rounds, they may have enough room. Last one I bought were around $10.