[1] Administratively Constable Bay and its surroundings belong to the Northeast Greenland National Park.

[2] Constable Bay lies in the northernmost shore of Peary Land, in Johannes V. Jensen Land, about 35 km (22 mi) west of Bliss Bay and about 5 kilometres (3.1 mi) east of Cape Morris Jesup.

It is a fairly large indentation, with Cape James Hill rising at its eastern end.

[3] The bay is clogged by fast ice the year round.

The northern arm of the Sif Glacier, discharging from the Roosevelt Range to the south, ends in a valley with its mouth in Constable Bay, having formed prominent terminal moraines.