The closest they come to a romantic moment is in Episode 25 of the anime, where Misa confesses her love for Light and kisses his hand. Light, however, is visibly uncomfortable and pushes her away, putting his own goals and plans above their relationship.
It's important to note that while Light and Misa's relationship is portrayed as romantic, it is ultimately unhealthy and manipulative. Light uses Misa's affection for his own ends, while Misa is blinded by her love for him.