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…)