One of the running problems that Saumarez had to face almost throughout his five years as Commander-in-Chief, Baltic, was the Eartholms. Their possible capture was a controversial issue and shows the degree of discretion given to Saumarez to make his own judgement. The events highlight the way in which a commander-in-chief can avoid taking action when he has doubts about its viability by throwing the decision back to the Admiralty or by procrastination and show differences between the Danish and the British reports of the action.

The Eartholms are a cluster of four small islands lying some ten nautical miles to the north-east of the island of Bornholm in the southern part of the Baltic. The two main islands lie close and parallel to each other. They form between them a natural deep-water harbour, divided into north and south, formerly by a connecting floating walkway but nowadays by a pedestrian bridge. One or other is accessible to sailing vessels under most wind conditions. Frederiksholm is some 300 yards long by 40 wide and Christiansø 400 yards by 155. The largest of the islands, Christiansø, is also the name by which they are generally called, but the official name is Ertholmene (from the Danish word ært [pea] which is what they are said to look like on a chart). There is only a thin covering of soil over the granite rock of which they are composed. Much of this was brought by ship from Bornholm, as today are the provisions and even, in a dry summer, the drinking water. Of the other two islands, one is little more than a large bare rocky outcrop; the second, Græsholm, was originally quite grassy, as the name implies. The commandant of the islands kept a cow there which, in good weather swam the narrow channel morning and evening over to the two main islands to be milked. Now Græsholm is a bird sanctuary and their droppings kill most of the vegetation.

Until the middle of the seventeenth century, nobody lived on the Eartholms: a few fishermen used them as a base for herring fishing in the late summer. However, in 1684, King Christian V of Denmark started to create a fortress there to defend the natural harbour, as a protection against the Swedish navy.