Today Wikipedia taught me that while Latvia and Lithuania didn’t maintain ones, Estonia had a government-in-exile during the Cold War:

[…] existing from 1944 until the reestablishment of Estonian sovereignty over Estonian territory in 1991–92. It traced its legitimacy through constitutional succession to the last Estonian government in power prior to the Soviet invasion of 1940. During its existence, it was the internationally recognized government of Estonia.

I did a quick search, and found this paper by Lauri Mälksoo published in the Nordic Journal of International Law back in 2000:

International legal practice in the 20th century is rich in challenging cases of state continuity and extinction, One of those cases is the preservation of the continuity of the Baltic states throughout 51 years of foreign occupation and annexation. After decades of non- recognition of Soviet annexation by leading Western powers, the present-day Baltic republics have not been seen as successor states of the Soviet Union, but as identical with the independent Baltic states of 1918-1940. How could the continuity of the Baltic states be preserved, especially as the Soviet Union had effectively and seemingly “forever” established its control over the Baltic republics?

He concluded:

This article focuses on the Estonian situation, laying out the events of 1944 which led to the proclamation of the new constitutional government, and after the country was for the second time occupied by the Soviet army, to the creation of an Estonian government in exile. One of the main questions asked in this article is whether and how the Estonian government in exile contributed to the preservation of the continuity of the Republic of Estonia. Both legal and political aspects played a role in the preservation of the continuity of the Republic of Estonia, and for various reasons, the role of the Estonian government in exile was not exactly that of “the” preserver of state continulty.