To "summon" or "summon up" usually does not mean to call someone, in the sense of calling on the phone or shouting. In a legal setting, it can mean to insist that someone appear for court or a trial, which is usually done by letter. But most often, "summon" or "summon up" are used as idioms to mean that someone forced or persuaded himself to do something difficult or unpleasant:
"After an hour of thinking about it, I summoned the courage to tell my boss I was quitting."
"Somehow, despite my own grief, I managed to summon a smile for the little girl who held my hand amid the rubble."
"Summon" here comes from the meaning of using magic or sorcery to conjure a demon (i.e., to force it to appear).