The Golden Globes
Samantha Eggar won the Golden Globe for Best Actress (Drama) for the best in film of 1965 over Julie Christie ("Darling"), Elizabeth Hartman ("A Patch of Blue"), Simone Signoret ("Ship of Fools") and Maggie Smith ("Othello").
Julie Christie won the Oscar, of course, and it was the same year as "Doctor Zhivago."
Still, Samantha Eggar's Golden Globe win is a hint that she might have come close to winning an Oscar. Like Julie Christie, she was young, fresh, beautiful and talented.