I don't know whether to post this here, but what do other countries have instead of coronations?
Depends on the country. Of the current European monarchies:
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Belgium
Belgium has no crown; the monarch's formal installation requires only a solemn oath on the constitution in parliament, symbolic of the limited power allowed to the king under the 1831 Constitution.
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Denmark
In 1660 the coronation ritual was replaced with a ceremony of anointing. This rite was in turn abolished with the introduction of the Danish Constitution in 1849. Today the crown of Denmark is only displayed at the monarch's funeral, when it sits atop their coffin. The present Queen, Margrethe II, did not have any formal enthronement service; a public announcement of her accession was made from the balcony of Christiansborg Palace,.
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Liechtenstein
Liechtenstein does not use a coronation or enthronement ceremony.
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Luxembourg
The Grand Duke of Luxembourg is enthroned at a ceremony held in the nation's parliament at the beginning of his or her reign. The monarch takes an oath of loyalty to the state constitution, then attends a solemn mass at the Notre-Dame Cathedral. No crown or other regalia exists for the Grand Duchy.
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Monaco
The Principality of Monaco does not possess any regalia, and thus does not physically crown its ruler. However, the Prince or Princess does attend a special investiture ceremony, consisting of a festive mass in Saint Nicholas Cathedral, followed by a reception where the new ruler meets his subjects
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The Netherlands
Although the Netherlands has a crown and other regalia, these have never been physically bestowed upon any Dutch monarch. Queen Beatrix of the Netherlands, like each of her predecessors, had an inauguration ceremony rather than a coronation.
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Norway
While the Norwegian constitution of 1814 required the King of Norway to be crowned in Trondheim, this mandate was repealed in 1908. Thereafter, the ruler has only been required to take his formal accession oath in the Council of State and thereafter in the Parliament. King Olav V instituted a ceremony of royal consecration, known as Signing til kongsgjerning. This ritual took place again in 1991, when King Harald V and Queen Sonja were similarly consecrated.
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Spain
No monarch of Spain has been crowned since John I of Castile and Ferdinand I of Aragon. Instead, the new monarch appears at the Cortes, where he or she takes a formal oath to uphold the Constitution. Although the crown is evident at the ceremony, it is never actually placed on the monarch's head.
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Sweden
The last coronation was Oscar II's coronation in 1873; subsequent kings of Sweden elected not to be crowned, though there is no law or constitutional provision preventing a coronation. Carl XVI Gustaf was instead enthroned in a simple ceremony. The crown jewels were displayed on cushions to the right and left of the royal throne, but were never given to the king.
Read more here -
Coronations in Europe - Wikipedia, the free encyclopedia