Both would need to make saves, or move at 1/4th Speed per turn, but a creature being forced into the area might not have a choice. Speed is the statistic from which your total movement is calculated from.
While grappled/grappling, your Speed is halved, as you are pulling/dragging the other creature, provided you’re physically capable of this forced movement.
Moving at half speed does not reduce your speed, and behooves many skill checks that require visual or auditory queues (such as stealth, perception, investigation.)
Average movement speed for most humanoids is 30ft. Half that from grapple is 15ft, you are burdened. Moving at 50% your current speed leaves you at 7.5ft (5ft if using the common 1″ grid movement.) One option to get around this is to apply an effect that adds speed (not movement) to one or both creatures.
Applying the speed bonus to one creature, in order to force the other to make the save is certainly an interesting, albeit sadistic tactic.
Eldritch Blast (Repelling Blast) could also trigger the save, provided you can force movement greater than half the creature’s speed.