In the old git-svn repo:
1) Find the revision where the local branch of interest branched off master:
git svn find-rev `git merge-base $branch master`
Here, master corresponds to subversion's trunk and $branch to the local branch we want to save.
merge-base says "Tell me the last commit these two branches have in common." It gives back the label (hash) of the commit. To learn more about it, run git show <hash>
svn find-rev says "Tell me the svn revision number for this git commit." You'll get back a number, such as 3456.
2) Create patch files for every commit on the branch:
git format-patch master..$branch
format-patch will produce a bunch of .patch files in your local directory, one for each commit between master and the tip of your branch. They start with numbers, in the order the commits were made, so that they can be applied in that order later.
In the new git repository:
After cloning the new git repository (goodbye svn!)
1) Find the commit that corresponds to the one where the branch started.
git log :/@3456
where 3456 is the revision number, @ is a symbol that happens to be before the revision in the commit log, and git log :/ means "show me the log starting from a commit with this text in its message."
You might have to search for your revision number to find the right one, in case that number happens to appear in other commit messages.
Copy the hash of the commit you find.
2) Check out that commit
git checkout <hash of commit found in previous step>
Now you're in detached head state!
3) Create the branch here, and check it out
git checkout -b $branch
Whew, head is attached again.
4) Apply the patches
git am ../path-to-old-git-svn-repo/*.patch
Now your branch exists on the new repository, as if you'd always been working from there.
 If you're not moving the branch from one git-svn repo to another, then find the destination commit like this:
git svn find-rev r3456
where 3456 is the revision number where the branch starts.