At this time the court fell into much extravagance in masquerading; both king and queen, and all the court, went about masked, and came into houses unknown, and danced there with a great deal of wild frolic. In all this people were so disguised, that without being on the secret none could distinguish them. They were carried about in hackney chairs. Once the queen's chairmen, not knowing who she was, went from her: so she was alone, and was much disturbed, and came to Whitehall in a hackney coach: some say it was in a cart. The duke of Buckingham proposed to the king, that he would give him leave to steal her away, and send her to a plantation, where she should be well and carefully looked to, but never heard of any more; so it should be given out, that she had deserted; and upon that it would fall in with some principles to carry an act for a divorce, grounded upon the pretence of a wilful desertion. Sir Robert Murray told me, that the king himself rejected this with horror. He said, it was a wicked thing to make a poor lady miserable, only because she was his wife, and had no children by him, which was no fault of hers.--From History of his own Times--
Other options that were suggested included polygamy.