After writing a couple of Daily Thoughts on the subject of the Queen of Sheba, the question was posed to me about whether Solomon might have fathered a child by her?
To answer this question, I must first of all point out that the Scripture does not say either yes or no on the matter. So opinion has to be based on clues only from the Holy Text, and how much reliability we want to place on outside pseudo histories and mythologies. It is harder to prove a negative than it is to prove a positive, so for the sake of our investigation let us assume we are seeking to find evidence to the case that progeny did issue forth from Sheba through a relationship with Solomon.
My first circumstantial evidence to the possibility of such an event occurring would be the fact of Solomon's conduct with regard to women. Of Solomon the Scripture records:
"But King Solomon loved many strange women, together with the daughter of Pharaoh, women of the Moabites, Ammonites, Edomites, Zidonians, and Hittites; Of the nation which the Lord said unto the children of Israel, Ye shall not go into them, neither shall they come in unto you: for surely they will turn your heart after their gods: Solomon clave unto these in love." (1Kings 11:1-2)
The evidence is that Solomon, because of his liking for women, ultimately having some seven hundred wives and three hundred concubines, was a man disposed toward sexual intimacy if it was offered. (1Kings 11:3)
My next piece of circumstantial evidence involves something that the Scripture has to say about the relationship that existed between Solomon and Sheba from the queen's perspective. That is the Scripture testifies that "…she communed with him of all that was in her heart." (1Kings 10: 2b) This is a dangerous thing for a queen to do, but is a common action for a woman who is either intimate or desires a deeper relationship with a man. Predatory men and those who have genuine liking or interest in women encourage such honesty. I am not saying Solomon was a predator, but it is plain he liked women. Self revealing conduct is a level of meaning to be found in the desire of a woman toward her husband that God pronounces will be the future of women after the temptation in the Garden. (Genesis 3:16) It includes both the physical and mental for the woman and it is often the case where one part of the person goes the other follows.
My next piece of evidence from the Scripture involves another account of the Queen of Sheba's actions. It begins "And when the Queen of Sheba had seen all Solomon's wisdom, and the house that he had built (possibly a reference to the Temple since his ascent to the Temple is mentioned)…there was no more spirit in her." (1Kings 10: 4-5) Some commentaries see this statement as an indication she fainted, but this interpretation is by no means certain and could it could also point to some sort of surrender of her self will or emotions to Solomon. If the former were the case it would not diminish my point as much as the latter would increase the likelihood of evidence for coitus between the two. Swooning has long been a means by which women could focus attention on themselves, but the reason of oriental opulence given for a legitimate swoon would seem unlikely. Whatever happened there is no doubt it caused Sheba to bestow material benevolence on Solomon, perhaps out of proportion to what she had intended when she came.
My final evidence from Scripture has to do with Solomon's response to the queen. The Bible says that King Solomon gave unto the Queen of Sheba all her desire. (1Kings 10:13) What this was we do not know, but we do know that what she desired was separate from the royal bounty which he also gave to her. The conclusion of something personal being delivered being making the queen pregnant with child is not out of the question. There are a number of reasons for the queen to desire such a child of Solomon if his influence, power, and wisdom is as great as the Bible says. Just two of them would be relations with the Kingdom of Israel and the another would be the producing of a child that would be a worthy successor to her throne.
Apart from the Biblical record there are a number of ancient accounts which claim that Solomon sired a child by the queen.
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Taken from: http://www.jonsquillministries.org/FAQSolomanSheba.htm