Ser Byron attempted to kill the dragon Syrax with the same approach as Serwyn of the Mirror Shield. He approached the dragon hidden behind his shield, so that all Syrax would see was his own reflection. The plan didn't work and he was killed by Syrax.
Grand Maester Munkun claimed that it was Vhagar that killed Byron, but this seems likely to be a mistake. Vhagar was ridden by Prince Aemond Targaryen, who was on the same side of the conflict as House Swann. Ser Byron's squire wrote a letter to his daughter, claiming that Syrax killed his master.