A number of modern place names in Greenland commemorate Gunnbjörn, most notably Gunnbjørn Fjeld.
It is stated that his sons lived in Iceland's West fjords and a note is made that Gunnbjörnssker are named after him.
He and his crew sighted islands (Gunnbjörn's skerries) west of Iceland, and reported this find but did not land.
The first records of purposeful visits to Gunnbjörn's skerries were made by Snæbjörn Galti around 978 and soon after by Erik the Red who also explored the main island of Greenland, and soon established a settlement.
[2][3] Waldemar Lehn (1911–2005), professor emeritus at the University of Manitoba and an expert in atmospheric refraction and mirages, argued that the skerries Gunnbjörn saw could be explained as the sighting of Greenland's coast via the refraction of a superior mirage.