Another word would be "regal". You might want to use "royal" because you can use it to describe the rank or manner of a king or queen. You could say "The queen performed here kingly duties", I suppose, but "royal"would be much better, as there is no question of gender. By the way "queenly" is also a word that means the same as "kingly" - but obviously for use with a queen.

Royal and Kingly are synonyms - pertaining to monarchs (either Kings or Queens).