AbstractWe study procedurally fair matching mechanisms that produce stable matchings for the so-called marriage model of one-to-one, two-sided matching. Our main focus is on two such mechanisms: employment by lotto introduced by Aldershof et al. (1999) and the random order mechanism due to Roth and Vande Vate (1990) and Ma (1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Furthermore, we correct some misconceptions by Aldershof et al. (1999) and Ma (1996) that exist on the probability distribution induced by both mechanisms. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism.