Cigar bands were a novel early 20th century way of promoting something. Here are 2 examples of these I uncovered.
My Grandfather's sister, my great aunt Juliet, did characterizations and impersonations on the Vaudeville circuits. During the early part of her career she went by the name Juliet ?. The implication being that nobody in the audience ever really knew if the performer on stage was her. Post World War I she became known as Miss Juliet. The photo of her on the cigar band is a promotional portrait of her that was taken around 1910.
The lower cigar band is part of a book which is a series of studies for this finished product. My Grandfather was a longtime member and Dean of the Friars Club. This band was given out with the cigars at one of the Friars many banquets or roasts.