King Saul was rejected as King by God for rejecting His Word. Is he in Hell?  How about King Solomon? He went to worship idols because of his wives. Is he in Hell?

Determining the salvation of others is always a tricky business. The two men you bring up certainly have an uncertain testimony. The scripture may not be completely clear as to their final abode. However, I have reasons for believing that both them were saved. I will explain briefly.

SAUL

Saul was certainly rejected by God. The Spirit of God that had guided him (1 Samuel 11:6And the Spirit of God came upon Saul when he heard those tidings, and his anger was kindled greatly.
See All...) departed from him when he rebelled against God (1 Samuel 16:14But the Spirit of the LORD departed from Saul, and an evil spirit from the LORD troubled him.
See All...). God refused to speak to Saul by any of the accepted methods (1 Samuel 28:6And when Saul enquired of the LORD, the LORD answered him not, neither by dreams, nor by Urim, nor by prophets.
See All...). However, an incident that occurred when Saul approached the witch of Endor has convinced me that he was probably saved. The witch was frightened when Samuel came up (1 Samuel 28:11-14 [11] Then said the woman, Whom shall I bring up unto thee? And he said, Bring me up Samuel. [12] And when the woman saw Samuel, she cried with a loud voice: and the woman spake to Saul, saying, Why hast thou deceived me? for thou art Saul. [13] And the king said unto her, Be not afraid: for what sawest thou? And the woman said unto Saul, I saw gods ascending out of the earth. [14] And he said unto her, What form is he of? And she said, An old man cometh up; and he is covered with a mantle. And Saul perceived that it was Samuel, and he stooped with his face to the ground, and bowed himself.
See All...). He was obviously not the familiar spirit she was used to receiving. The Bible text calls him Samuel (v.12, 15). Certainly, this was an actual appearance by Samuel. Notice a verse from what Samuel told Saul:

1 Samuel 28:19Moreover the LORD will also deliver Israel with thee into the hand of the Philistines: and to morrow shalt thou and thy sons be with me: the LORD also shall deliver the host of Israel into the hand of the Philistines.
See All... Moreover the LORD will also deliver Israel with thee into the hand of the Philistines: and to morrow shalt thou and thy sons be with me: the LORD also shall deliver the host of Israel into the hand of the Philistines.

Saul and his sons will be with Samuel by the next day. Samuel was evidently in Abraham's bosom (as was Lazarus in Luke 16:22-23 [22] And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried; [23] And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom.
See All...).  Everything about Jonathan, one of Saul's sons, points to him being saved.  Samuel states that Saul and his sons would be with him--that is, where Samuel was. I do not think this would be possible if Saul went to hell.  By the way, I realize that many will think that Samuel is simply referring to the place of the dead. That is a possibility, but I still do not think it makes as much sense. The phrase "with me" is just too strong.

SOLOMON

Solomon also got himself into deep trouble with God. However, I think he was probably saved. Instead of a long argument, let me give just one verse:

Nehemiah 13:26Did not Solomon king of Israel sin by these things? yet among many nations was there no king like him, who was beloved of his God, and God made him king over all Israel: nevertheless even him did outlandish women cause to sin.
See All... Did not Solomon king of Israel sin by these things? yet among many nations was there no king like him, who was beloved of his God, and God made him king over all Israel: nevertheless even him did outlandish women cause to sin.

This verse recognizes the sin of Solomon while at the same time declaring him "beloved of his God." I just do not see how this statement could be made of a lost man.

Just remember, these men lived before the universal indwelling of the Holy Spirit. They could lose the Spirit without losing their salvation.  They were simply required to die "in faith" (Hebrews 11:13These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth.
See All...). Though I accept that I could be wrong on this, I believe they both are saved.