Sing each other's praises, run up to the climate summit

They sang each other's praises in the run up to the Copenhagen climate summit, but China and the United States traded sharp barbs in a superpower standoff that has helped set the UN talks on edge. On key issues ranging from how to share out the burden of slashing greenhouse gases, whether such efforts should be independently verified, or if the United States owes developing countries -- including China -- a "climate debt," the world's two largest carbon polluters were at loggerheads.

Could you please explain to me what "run up" and "sang each other's praises" means in this context?