The heart-shaped crystal Edward gave her was a representation of himself so she'd always think of him, too. The heart was like he said, just like him.
Edward: "But I thought it was a good representation. It's hard and cold. And it throws rainbows in the sunlight."
Bella: "You forgot the most important similarity. It's beautiful."
Edward: "My heart is just as silent. And it, too, is yours."