The SCA does a lot of re-enactment fighting, but they wear heavy armour and fight to full contact, using taped rattan blades.

There are a shedload of other medieval/renaissance re-enactment groups that do live steel fighting, though - I'm in one of them.

If you're trying to find a group like this, just look for your local SCA barony/shire/kingdom on the internet. They're a worldwide group, so there's bound to be one in your area.