Sforno on Exodus
לזכרון לפני ה' תמיד. In order for G’d to always remember the merits of the founding tribal fathers of the Jewish people and to treat their offspring favourably when remembering their founders.
Chizkuni
בחשן המשפט, “on the breastplate of judgment;” the term “judgment” here refers to the High Priest being able to receive answers to queries on Jewish law from G-d when these require to be clarified.