Judy Garland only performed “Over The Rainbow” twice during her many television appearances, which spanned 14 years. She performed it on her first TV Special, “Ford Star Jubilee” in the episode called “The Judy Garland Special” in 1955, and sang it to her children on The Christmas Edition of her weekly TV show “The Judy Garland Show” (1963).
Here Judy is dressed up [in the first special] as the tramp character she played when doing a duet with Fred Astaire in the film ‘Easter Parade’.
Watch. It shows why she was both a great singer and a great actress.