From SuspireWiki

Definition: A formal duel with potentially fatal consequences. Such duels may be fought to Final Death or to simple injury. Traditionally such duels are a matter of honor of trial by combat.

Tradition states that, in years gone by, the Invictus used formal duels, contests and trials by ordeal to settle otherwise unsolvable disputes. These duels are known collectively as monomacy. Some members of the covenant believed, as mortals did in the Middle Ages, that God stepped in and ensured that the victory went to the righteous party. Other members simply wanted a means whereby elders could settle personal disputes without dragging pawns and even entire domains into the battle. By modern nights, the Invictus has largely abandoned its claims of divine right, but monomacy is still practiced when a just cause arises.