The 71-year-old star - who received the Outstanding Performance by a Female Actor in a Leading Role in a Motion Picture award for her performance in 'The Wife' - wanted to pay tribute to her relative to recognise her unfulfilled ambition of becoming an actress.
And Glenn admitted she felt she was "carrying" all the previous generations of women in her family who had been unable to pursue their dreams outside of the home.
She told People magazine on the silver carpet at the Shrine Auditorium in Los Angeles: "This here is my grandmother's wedding ring and she wanted to be an actress and I only knew that after she died.
"She never would have been allowed to do that. I feel like I'm carrying the women in my family who were wonderful mothers and wives, but could have had more personal expression probably."
As well as the ring, Glenn also accessorised her cream double-breasted Ralph Lauren suit with Cartier jewels and Giuseppe Zanotti shoes.
When she picked up her award later in the evening, the 'Fatal Attraction' actress praised the "power" of film.
She said: "One of the most powerful things we have as two human beings is two eyes looking into two eyes and film is the only art form that allows us the close-up and it substitutes for real life two eyes looking into two eyes.
"I think we have to remember how powerful that is in a world that is consumed with different size screens, that all we have are two human eyes looking into two other eyes, that will give us empathy and understanding."