Yes, Easternmost should be capitalized when referring to a specific location on the easternmost point of something, such as a country or territory.
Maine is the easternmost state of the USA.
The easternmost point on the North American continent is Cape Spear in Newfoundland, Canada. It is also the easternmost point in North America.
The easternmost point in Iceland is approximately 13.49° West longitude.
Alaska. At 179°37' East, the easternmost tip of Semisopochnoi is the easternmost land location in the United States, and is arguably the easternmost location in North America. Semisopochnoi sits only 23 minutes west of the 180th meridian and therefore is in the Eastern Hemisphere
Easternmost point - Hvalbakur, Suður-Múlasýsla:Latitude: 64°35′NLongitude: 13°14′W
Maine is the easternmost state in the United States. It is unique because it is the closest state to Europe and is known for its rugged coastline, dense forests, and cold climate. Maine also has the easternmost point in the contiguous United States, West Quoddy Head.
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It has to be somewhere in the neighborhood of Eastport, Maine ... the easternmost point in the continental US.
West Quoddy Head in Lubec, Maine is the easternmost point of the United States and the closest point to Africa from a point in the fifty States