Sterling and silver-plate flatware scratches when pieces knock against each other and tarnishes faster when exposed to open air, so the goal is separation and a sealed environment, not just a box.
Pro tip: Anti-tarnish strips are inexpensive and can be tucked into the box alongside the wrapped set for extra protection during longer moves or storage.
Watch out: Silver pieces stacked directly against each other without a cloth barrier scratch from simple friction during a bumpy ride.