 If you liked
Shigatsu wa Kimi no Uso
|
 ...then you might like
Ongaku Shoujo
|
"Your Lie in April" / "Shigatsu wa Kimi no Uso" and "Ongaku Shoujo" both centre around a very cheerful blonde girl attempting to convince the rather shy protagonist with a case of stage fright to continue to pursue music. As the two characters grow closer, the formerly troubled protagonist slowly comes out of his/her shell but becomes dependent on the new friend.
Also, in both anime, there involves a cat at the very beginning and melodrama at the end.