There's a lot of potential suggestions in this category, but perhaps you could first give us a list (MAL?) of what you have already seen in the romance genre? Would help
For starters though, the first thing that came into my head when I read "heart-warming romance" was
Kimi ni Todoke. It's a shoujo school romance that is just plain adorable at times.
Drop a post with your viewed list and I'll suggest a few more suitable candidates...