Looking for a romance where one of the them really looks up to the other. 

Thanks :)

That Fool One was a fan of the other. The main character was really endearing and it was a light and fun drama.
Nodame cantible (female lead is like a puppy that follows the male lead around)
runaway sweetheart (female lead is a fan of and inspired by the male lead)
dream high and what's up both feature relationships that are fan/role model-ish based
This one is what you would call a golden oldie! :-) - Star no Koi