Shakespeare in Love doesn't load up on the symbolism… maybe because it's too busy throwing Shakespeare-related puns at you.
The only recurring object in the movie is a minor one: the snake bracelet prescribed to Will by his doctor:
"The woman who wears the snake will dream of you, and your gift will return."
It's a mystic charm intended to provide Will with a muse. He gives it to Rosaline, who betrays him. "I would have made you immortal," he said, which is significant because the snake bangle is almost an Ouroboros—the snake devouring its own tail, and a symbol of infinity.
However, the bangle is broken by Burbage (say that five times fast) sealing Rosaline's fate as Will's anti-muse. She is immortalized… but just not as the heroine.