Resolving Composer merge conflicts when upgrading Symfony2 Standard Edition
I would say the best/ideal case is if you have somewhat stable requirements (not full of dev-master..), then you can just rm the composer.lock (or git checkout) and run update to make sure you get latest dependencies of everything.
If that's not possible, then you can also just revert the changes from upstream, and composer update <specific packages> to bring them up to speed. That is however error prone and tedious, so I think the best really is to make sure you have strict enough dependencies in your project that you can run composer update without fear.