Off the top of my head, I think
Scryed fits the bill although I'm a bit hazy on its romantic elements.
Nadesico might meet the requirements, but I'm sure you've already seen it.
There's Outlaw Star, but the growth of the main character's fighting skills are more subtle than the power ups that you would see in dragon ball or gundam seed.
Also, Hajime no Ippo (boxing) might also work but it's been so long since I've last seen it that I can't remember how much romance there was.