Conversation so far:
Did Dimitri Tiomkin win any awards for High Noon?
The film received seven Academy Award nominations and won four awards, including two for Dimitri Tiomkin: Best Original Music and Best Song.
Who directed the film High Noon?
Fred Zinnemann.

Question: what was the name of the song he won the Best Song award for?
Self-contained rewrite: What was the name of the song Dimitri Tiomkin won the Best Song award for?