When you run out of options
Once Paul arrived in Rome, he called for the Jewish leaders, and explained why he was there, that the Jews in Jerusalem made accusations against him, but that the Romans found him innocent,
“who, when they had examined me, wanted to let me go, because there was no cause for putting me to death. But when the Jews spoke against it, I was compelled to appeal to Caesar, not that I had anything of which to accuse my nation” (Acts 28:18-19).
Although the Romans found him innocent, they would not release him, so he appealed to Caesar, the highest authority in the land.
However, Paul did not want his Jewish brethren to think that he had something to accuse against them, because he wanted an audience with them, that he might preach to them.