In Sweden we'll write 13:00. How we say it depends on context. If someone asks what time it is the answer will probably be "ett", meaning one. Most people will figure out if it's afternoon or night by themselves.
If you ask what time TV show starts or a train leaves the answer will be "13:00", just as it's written. And then we mean one sharp, not 12:59 or 13:01.
If you ask what time TV show starts or a train leaves the answer will be "13:00", just as it's written. And then we mean one sharp, not 12:59 or 13:01.