I thought
Kamisama Hajimemashita was a cute and fun romance. Same director as
Fruits Basket.
I don't know if it meets the requirements of being "very romantic," but I'll suggest
Nodame Cantabile anyway. Romance is just one part of the package. All three seasons are packaged together in
this torrent, or you can watch the first season streamed with English dubbing at
Crackle.