Roast some of the plums alongside the chicken. The remaining plums should be roasted on a separate baking sheet for a side dish.
Preheat oven to 450 degrees. Season chickens with salt. Stuff each cavity with 2 sprigs rosemary. Tie legs together with kitchen twine. Place each chicken in an ovenproof skillet (preferably cast-iron), and place 2 sprigs rosemary around each chicken. (Alternatively, you can also roast the 2 chickens together in a roasting pan.) Toss plums with honey in a large bowl.
Roast chickens for 20 minutes. Remove from oven, and scatter some of the plums around chickens. Return to oven, and roast for 20 minutes more. Spread remaining plums on a rimmed baking sheet, dot with butter, and top with remaining 2 sprigs rosemary. Transfer to oven. Continue to roast chickens until an instant-read thermometer inserted into thickest part of the thigh reads 165 degrees; meanwhile, roast plums until soft and brown around edges, about 25 minutes. Let chickens rest for 10 minutes before serving.