It is always possible to jam RF communications given sufficient power. Lasers require line of site, which is normally a problem for Soldiers. Sometimes you need to get the message through. In WWI, they used runners. We can use machines to physically carry the message. This might take the form of drone, a ground robot, or a mortar round. It flies over to friendly lines until it overcomes the jamming and relays the message, or it might make physical contact with the network for a massive data transfer. This device would have to make use of a transponder so that friendlies know not to shoot it down.
The flip side of this is the kinetic jammer that is launched into the middle of enemy lines during the assault. It deploys its parachute over enemy territory and activates its thermal battery, broadcasting high power EW until the battery runs out. Repeat as needed until the enemy is overrun.
It recycles the obsolete idea of a courier to address 21st century problems.Add Improvement
It represents a way to get the message out regardless of the amount of electromagnetic jamming.