Energy is conserved in all GR solutions that possess a time-like Killing vector. (I.e., in static, non-expanding, non-contracting spacetimes.)
Schwarzschild and Kerr metrics have these vectors, and therefore there is global energy conservation in those spacetimes.
Also, there are still energy conditions (e.g., the null energy condition) that ought to hold even in non-energy-conserving spacetimes, which is why we can't just keep pulling things out of the quantum vacuum for free.
But John will understand these issues more deeply than I do, if what I've posted here isn't enough (or isn't rigorously true).