In the context of the Fate universe, "saving Saber's heart" refers to the process of convincing her to abandon her self-sacrificial and tragic wish for the Holy Grail. Saber's Wish - A Fateful Birthday, a fate/stay night fanfic

"Saber heart" most commonly refers to a pivotal narrative theme in the franchise regarding the emotional salvation of the character Saber (Artoria Pendragon). It also appears as a localized community term for school spirit and compassion in certain educational districts. Thematic Meaning in "Fate/stay night"