Both of these phrases refer to putting your self in a difficult or dangerous position for the sake of somebody else, such as owning up to doing something you did not do, to save somebody else being in trouble hence" putting your neck on the line" The "line " may refer to a time when people would have to put their neck in a certain position to have their heads chopped off !

"put his neck on the line for me" >>> willing to risk one's life for someone.

It's very hard to understand the meaning of the sentences,maybe you can show me the context,It will be helpful.