A note for my own reference, as I always forget how to create a remote branch then work with it later:
Create a new remote branch topic/add_awesomeness with, e.g.:
git push origin :origin:refs/heads/topic/add_awesomeness
Create a new local branch to track it:
git checkout --track -b add_awesomeness origin/topic/add_awesomeness
The unintuitive way to delete a remote branch is:
git push origin :heads/topic/doc_cleanup
(There must be a better way than that…)