Marilyn was never awarded with an Oscar, neither while she was alive, nor posthumous.The official recognition came from elsewhere : France and Italy rather than the USA (Awards).
On March 29, 1951 she appeared for the first and last time at the Academy Awards ceremony, at the Pantages Theater (6233 Hollywood Boulevard), where she presented the Best Best Sound, Recording Award to Thomas Moulton, for his performance in "All About Eve" (1950).
With Thomas Moulton
The master of ceremony was Fred Astaire.
Marilyn hoped to win an Oscar twice : as Best Actress in "Bus Stop" (1956) and in "Some Like it Hot" (1959).
But she didn't reach her hopes; in 1956 Ingrid Bergman won the Oscar ("Anastasia") and in 1959, it was Simone Signoret in "Room at the Top".
Some movie columnists twice suggested to give her a posthumous Oscar for her career, first in 1965 then in 1975.