The National Bird of Denmark is the Mute Swan. It Scientific Name is Cygnus olor. It was Officially Adopted in 1984, replacing the Skylark Alauda arvensis.
So far as I can determine the swan was not officially granted status as the National Bird of Denmark by law but by a popular vote held by either Danish Television or Denmark Radio.
The male Mute Swan (known as the cob) is generally larger than the female Mute Swan (known
as a pen) and is also distinguished by a larger knob on its beak.
1. http://www.fyidenmark.com/National_Bird_of_Denmark.html
2. http://www.10000birds.com/what-is-the-national-bird-of-denmark.htm