Gunhilda was a daughter of King Cnut the Great (985/95 – 1035), ruler over the Anglo-Scandinavian North Sea Empire, and his second wife Emma of Normandy (c. 985 – 1052).

Her engagement with Henry III, the son and heir of Emperor Conrad II and his consort Gisela of Swabia, was part of a pact of her father Cnut over peaceful borders of the Danish Duchy of Schleswig with Imperial Holstein in the area of Kiel.

Conrad temporarily had evolved plans to marry his son with Zoe Porphyrogenita, a daughter of the Byzantine Emperor Constantine VIII.

According to the chronicles of Alberic de Trois-Fontaines and William of Malmesbury, Gunhilda was accused of adultery and defended in trial by combat, but after her champion's victory she disdained the success and became a nun.

Stuck in a fierce conflict with quarrelsome Archbishop Aribert of Milan, Conrad asked his son for support and both Henry III and Gunhilda followed him on his expedition.