In November 1677, Anne's elder sister married a Dutch prince, William of Orange, but Anne could not attend the wedding, as she was confined to her room with smallpox.[14] By the time she recovered, Mary had already left for her new life in the Netherlands. Lady Frances Villiers contracted the disease, and died. Anne's aunt Lady Clarendon (the wife of Henry Hyde, 2nd Earl of Clarendon) was appointed as her new governess.[15] A year later, Anne and her stepmother visited Mary in Holland.[16] Anne's father and stepmother retired to Brussels in March 1679 in the wake of anti-Catholic hysteria fed by the Popish Plot, and Anne visited them from the end of August.[16] In October, they returned to Britain, the Duke and Duchess to Scotland and Anne to England.[17] She visited her father and stepmother in Scotland from July 1681 until May 1682.[18] It was her last journey outside England.[19] Anne's second cousin George of Hanover (her eventual successor) visited London for three months from December 1680, sparking rumours of a potential marriage between them.[20] Historian Edward Gregg dismissed the rumours as ungrounded, as her father was essentially exiled from court, and the Hanoverians planned to marry Prince George to his first cousin Sophia Dorothea of Celle as part of a scheme to unite the Hanoverian inheritance.[21] Other rumours claimed she was courted by Lord Mulgrave (later made Duke of Buckingham), although he denied it. Nevertheless, as a result of the gossip, he was temporarily dismissed from court and despatched to Tangier.[22] On 28 July 1683 in the Chapel Royal, Anne married the Protestant Prince George of Denmark, brother of King Christian V of Denmark (and her second cousin once removed through Frederick II).[23] Though it was an arranged marriage, they were faithful and devoted partners.[24] They were given a set of buildings in the Palace of Whitehall known as the Cockpit as their London residence,[25] and Sarah Churchill became one of Anne's ladies of the bedchamber.[26] To mark their friendship, and at Anne's request, Anne and Sarah called each other the pet names Mrs. Morley and Mrs. Freeman respectively rather than use their formal styles and titles.[27] Within months of the marriage, Anne was pregnant, but the baby was stillborn in May. Anne recovered at the spa town of Tunbridge Wells,[28] and over the next two years, she gave birth to two daughters in quick succession, Mary and Anne Sophia.[29]

His marriage to Anne was arranged in the early 1680s with a view to developing an Anglo-Danish alliance to contain Dutch maritime power. As a result, George was unpopular with his Dutch brother-in-law William of Orange, who was married to Anne's elder sister, Mary. William and Mary became joint monarchs of Britain, with Anne as their heiress presumptive, in 1689 after the "Glorious Revolution" deposed James II and VII, the father of Anne and Mary. William excluded George from active military service, and neither George nor Anne wielded any great influence until after the deaths of William and Mary, when Anne became queen. During his wife's reign, George occasionally used his influence in support of his wife, even when privately disagreeing with her views. He had an easy-going manner and little interest in politics; his appointment as Lord High Admiral in 1702 was largely honorary. Anne's seventeen pregnancies by George resulted in twelve miscarriages or stillbirths, four infant deaths, and a chronically sick son William, who died at the age of eleven. Despite the tragic history of their children, George and Anne's marriage was a strong one. He died aged 55 from a recurring and chronic lung disease, and was buried in Westminster Abbey.