Princess Sophie of Sweden (1801 - 1865) daughter of King Gustav IV of Sweden who was 8 years old when her father was deposed and later married Grand Duke Leopold of Baden. Likewise her sister, Princess Cecilia of Sweden (1807–1844) married Grand Duke August of Oldenburg.
Do men count? Franz Ferdinand, Duke of Hohenberg a morganatic grandson of Archduke Franz Ferdinand of Austria married Princess Elizabeth of Luxembourg the daughter of Grand Duchess Charlotte of Luxembourg and her Husband Prince Felix of Bourbon-Parma
As previously stated, it seems to have become an increasingly declining practice for princesses from large, reigning, and royal houses to leave their countries to marry foreign princes. King George III of Great Britain, remembering the unhappy experience of his youngest sister (born Princess Caroline-Mathilde of Wales) in Denmark, as queen consort to King Christian VII, was very grudging toward his own daughters' marriages. A possessive father by nature, he couldn't bear to part with them: this meant either not marrying ever (as was commonly the case with princesses who stayed home) or marrying men of lower rank (socially unacceptable). As it was, they all married relatively late -- some not even until their father had descended into mental decline, and a regency was declared.
Viewing the matter from the opposite standpoint: the Duchess of Edinburgh (daughter-in-law of Queen Victoria) was known to suffer intense bouts of homesickness, while living in her adopted land. As such, she never missed an opportunity to pay visits to her native land (she was born Grand Duchess Maria Alexandrovna of Russia). Her Romanov cousin (Grand Duchess Olga Constantinovna) had the same problem in Greece, where she arrived as a child bride in 1867 to become the queen consort of King George I.
This reluctance or resistance to leave home, however, does not appear to have characterized members of smaller -- even if reigning -- dynasties: Germany had duchies, grand duchies, and principalities with a plethora of eligible princesses who readily left home to marry foreign royals. The prospect was all the more enticing when they managed to nab king husbands. The same could basically be said of even some smaller royal dynasties (e.g. the kingdom of Portugal, where the daughters of Queen Maria II never expected to succeed to the throne, since they had numerous brothers).
Sometimes the princess who left a large kingdom was not really a dynastic member of the said kingdom but rather, a foreign morganaut (e.g. the Battenberg princesses). So they really didn't have anything to *lose*, since they were already displaced quasi-royals: for Ena, the prospect of being elevated from a morganatic to royal status, epitomized by queenship, was too great to pass up when presented with an opportunity to become the consort of King Alfonso XIII of Spain. But for nothing less would she have been willing to leave Great Britian. Her cousin Louise was a more modest person in her royal ambitions: as it was she, too, managed to land a foreign king (Gustaf VI Adolf of Sweden).
A similar thing could be said of dynastic members of NON-reigning royal (even "large") houses -- e.g. Orléans, Two Sicilies. Such persons were already foreigners living in exile. As members of deposed dynasties, they found themselves uprooted from their native lands, and hence had to seek refuge in whatever places they could find which would accept them with courtesy.
Emperor Franz Joseph of Austria-Hungary, for instance, was known to offer a hand of hospitality to a number of displaced royals -- e.g. Parma, Two Sicilies. He even approved, for dynastic reasons, marriages between Habsburgs and members of such houses, whom he regarded as *equals*.
Bearing all this in mind, I thought of coming up with a list of exiled members of deposed houses who were able to contract good dynastic marriages, taking full advantage of their claim to *equality*, while at the same time not being encumbered with being tied down to the native lands from which they had already been uprooted.
Princess Maria Annunziata of Bourbon-Two Sicilies (daughter of King Ferdinando II), for instance, married (as his second wife) the Austrian emperor's brother Karl Ludwig, and became the mother of Archduke Franz Ferdinand (who married Countess Sophie Chotek morganatically and eventually died by assassination) and Archduke Otto, father of the last emperor.
Princess Zita of Bourbon-Parma later married Karl, the archduke who became that last emperor of Austria-Hungary. Her brother Felix became the consort of the Grand Duchess Charlotte of Luxembourg. Princess Amélie of Orléans became the queen consort of King Carlos I of Portugal. Her aunt Mercedes was briefly queen consort of Spain, as the first wife of King Alfonso XII.
Can anybody else name examples of exiled royals who made good dynastic matches?