Wikipedia
In the history of Portugal, a Miguelist (in Portuguese Miguelista) was a supporter of the legitimacy of the king Miguel I of Portugal. The name is also given to those who supported absolutism as form of government, in opposition to the liberals who intended the establishment of a constitutional regime in Portugal.
Miguel was regent for his niece Queen Maria II of Portugal, and potential royal consort. However, he claimed the Portuguese throne in his own right on the grounds that the "Fundamental Laws of the Kingdom" deprived his elder brother Pedro IV of his right to reign (and of any right of Pedro's daughter to inherit the kingdom from her father) when Pedro became sovereign of the former Portuguese colony of Brazil and launched war on Portugal to oust Miguel as a usurper.
This overall led to a political crisis, during which many people were killed, imprisoned, persecuted or sent into exile, culminating in the Portuguese Liberal Wars between authoritarian Absolutists (led by Miguel) and progressive Constitutionalists (led by Pedro).
In the end, Miguel was forced from the throne and lived the last 32 years of his life in exile.
Miguelism is based not only on the premise that Miguel and his line have legitimate right to the Portuguese throne, but also on defense of the traditional principles of a conservative monarchy based in Roman Catholic values and in the absolute power of the king, in contrast to the Enlightenment values.