In Linux:
$ sudo docker ps -aqf "name=containername"
Or in OS X, Windows:
$ docker ps -aqf "name=containername"
where containername is your container name.
To avoid getting false positives, you can use regex anchors like so:
docker ps -aqf "name=^containername$"
explanation:
-q for quiet. output only the ID
-a for all. works even if your container is not running
-f for filter.
^ container name must start with this string
$ container name must end with this string