According to the wiki:
So with ~500 HP and 20 Presence, I should be healing on a crit about 45 HP with a crit but instead I'm healing around 26 HP. Either the wiki is wrong or the heal calculation on the sword is wrong.The wielder will recover [5% of their Max HP + Presence] upon critically hitting a target. The critical hit must be a weapon hit from the Swift Sword for the special effect to occur.