Zebra finch courtship includes both the song and a courtship dance that is "directed" towards the female. Desmond Morris described it as follows:
The singing, posturing male advances towards the female in a rhythmic, pivoting dance. The exact form of this dance varies and is often obscured by the particular arrangement of branches upon which the birds are situated. It is best understood when it occurs along one long , straight branch. As the male advances towards the female down the branch, it swings its body from side to side, turning first to the left and then to the right, changing the position of its feet as it does so (Behaviour, 1954, 7:1-31).  

The video clip available here shows male LB60 directing several song strophes to a female that was in a separate cage behind a plexiglass partition immediately adjacent to the left edge of the video frame in the image below. This image is one frame from a 5-second QuickTime video.

Note: this is a large file (10.8 MB) and will take several seconds to download.