Personally I do a thorough set of joint rotations and arm swings in all directions.
The goals are to raise the temperature of our body (particularly our shoulder girdle and trunk), get synovial fluid flowing in the joints, detect any joint or muscle issues before we get started with an external load, and do a little bit of mobility improvement (perhaps "ungluing" some tissue, as Kelly Starrett says) so that we are sure to safely hit our entire range of motion. Joint rotations, maybe some jumping or running around, and arm swings hit all those goals for me.
Getting these points out of the way allows us to safely do our activity-specific warm-up, which is to say, pressing weights that are very light for us.