Final answer:
Estonia is the country that has the Saaremaa and Hiiumaa islands. These islands are located in the Baltic Sea off the west coast of Estonia, which is one of the three Baltic states.
Step-by-step explanation:
The country that has both Saaremaa and Hiiumaa islands off the west coast of it in the Baltic Sea is Estonia. These islands are the largest Estonian islands in the Baltic Sea. Estonia, one of the Baltic states, gained independence from the Soviet Union in 1991 and has since transitioned to a market economy with a democratic government. As a member of both the North Atlantic Treaty Organization (NATO) and the European Union (EU), Estonia has integrated its economy more closely with Western Europe, moving away from its Soviet-era connections.