git describe --contains $committish"$committish" shows a reference to the commit built on a tag plus a ~$n ancestorhood count, so the following command shows the most recent tag that contains a commit:
git describe --contains "$committish" | sed 's/~.*//'
If there is no tag that contains this commit, git describe will fail. If you'd like to get the (abbreviated) committish instead, add the --always option.