I can answer the 747 question: nothing really, it’s already designed for the contingency. The nose gear is designed to still function run-flat if a blowout occurred, and the main gear has so many tires that it would be barely noticeable. If it occured prior to takeoff, the plane would not be allowed to fly until the tire was fixed.
Worst case is during very-hard-braking emergencies, when the brake disks can get white-hot, and a fire can result. A fire can ultimately explode a tire because of the high pressure in the tires.
Note that a Concorde-type incident (tire pieces getting sucked into the engine) can’t happen on a 747 with the main gear (which are located aft of the engine inlets).