First I can think of: don't create situations where error can happen. Compile with exceptions turned off. Out of memory? Terminate the process/thread.
Another: create your objects using some factory, make constructor empty and initialize class by said factory once instance is already created (perhaps recursively instantiating its members). This way all error generating code will be moved outside of constructor.
See how Google approach it: https://google-styleguide.googlecode.com/svn/trunk/cppguide....