I really liked Kim Stanley Robinson's Ministry for the Future as a guide to think through the effectiveness of various carrots and sticks in staving off the climate catastrophe. It's a work of fiction set in the very near future. The carrots include a carbon coin that is paid out to those who sequester carbon emissions, for instance by leaving oil in the ground.

I don't recall courts being one of the sticks, but notably targeted assassinations of the worst climate perps are.