Were these principles given to Moshe Rabbeinu on Har Sinai with the specific instruction that they be incorporated into a calendar when the Sanhedrin would be disbanded? Or perhaps Moshe Rabbeinu was simply given general instructions to develop a calendar that would meet certain requirements (that Pesach be in the spring and so on) with the specific details left to Sages of future generations to develop as necessary.
Down To All The Details
The Brisker Rav maintained that even the specific details of developing the calendar were given to Moshe Rabbeinu on Har Sinai (Chiddushei Maran Riz HaLevi: Kiddush HaChodesh, Yoma, Sukka p. 8). The Chazon Ish, however, believed that Moshe Rabbeinu was only given general instructions to develop a working calendar, and the details were left to the Sages of future generations to work out (see Chazon Ish, O.C. 140: 3).
Rabbenu Saadiah’s View
Interestingly, Rabbenu Saadiah Gaon writes that even in the times of the Sanhedrin, beis din made use of a calendar to predict when the new moon would appear. Testimony was only used to comply with the requirement that witnesses must testify.