Please do provide some examples.
For starters, Eve Levin speaks of the following unions in her book Sex and Society in the World of the Orthodox Slavs, 900-1700
A number of Serbian and Bulgarian rulers contracted marriage alliances with Turkish leaders in an attempt to forestall conquest. Such unions violated canons against intermarriage with non-Orthodox. The Serbian prince Stefan Lazarevic, for example, married is sister to the sultan Bajazid in 1390. Despite the religious differnce, the Church and the nobility approved the union. Stefan Lazarevic was canonized, and the author of his vita praised him for arranging the marriage “in order to save the Christ-loving flock from the wolves”. The Bulgarian princess Tamara was married to the Turkish sultan Murad I in 1375, and the Serbian princess Mara Brankovic to Murad II in 1435. Far from condemning these marriages, Serbian and Bulgarian sources, including those of the Church, praised the positive influence each of these women had at the Turkish court. Mara, for example, was credited with facilitating the transfer of the relics of St. Ivan Rilski from Trnovo to Rila. The Orthodox brides’ refusal to apostacize to Islam certainly made these marriages more palatable to the Church.
They were, however, only following in the footsteps of the Byzantine emperors themselves. In his Grand Strategy of the Byzantine Empire
, Edward N. Luttwak devotes a chapter to marital alliances. Among others, he notes:
--Justinian II, who in 695 married the sister of the Khazar qagan Busir Glavan.
--His son, Leo III, married his son Leo IV, to the daughter of the Khazar qagan;s daughter to cement an alliance against the Saracens (though this princess converted to Christianity and became the pious Empress Irene.
--She betrothed her son, Constantine VI, to Rotrud, daughter of Charlemagne,but Irene later broke the engagement (and deposed her son).
--Emperor John Tzimiskes, "White Death of the Saracens, married his niece, Theophano, to Otto II, King of the Germans, in 972.
--John II Komnenos married his daughter to Kind Ladislas of Hungary in 1120.
--His son, Manuel I Komnenos, married Bertha of Sulzbach, sister-in-law of Conrad III of Germany and daughter of Raymond of Antioch, formerly of Aquitaine.
--Manuel VIII Palologos married his daughter Euphrsyne to Nogai, son of Baul, son of Jochi, son of Jenghiz Khan himself.
--Another daughter, Maria Despina Paleologina, was betrothed to Hulegu, destroyer of Baghdad; when he died, she married his son, Abbakha, another great grandson of Jenghiz Khan. This marriage was extremely successful, both from a personal and a diplomatic standpoint. On the one hand, the couple seemed very happy together; on the other, she used her influence to protect Byzantine interests, especially against the Seljuk Turks.
Sidebar: So revered was Maria Despina that, after her death, a church was erected in her memory. It stands still, to this day, in the Phanar Quarter near the Golden Horn: Panaghia Muchliotissa
, "All Saints of the Mongols".