A Special Event Hat is a something which Luna Lovegood apparently wears at special events.

During the 2014 Quidditch World Cup, Rita Skeeter suggests that Luna's husband Rolf was holding her hand mainly to keep her from putting such a hat on.

In 1995, Luna notably wore a large lion-shaped hat for a Quidditch match between Gryffindor and Slytherin; the hats which Skeeter refers to were presumably similar.