How about an engraved necklace? You could have a saying she loves etched into the metal of the necklace.
I gave my 9-year-old daughter a necklace that says, “I love you to the moon and back.” She loves it. You’d probably want a more grown-up saying for a 15-year-old, but I bet your daughter would love having a special message she could wear with her at all times. Every time she put it on, she would think of you.
Another idea would be a piece of jewelry with her birthstone on it. It would be more affordable than a diamond, but it would still be a nice piece of jewelry.
Let us know what you decided on, and how she liked it!