I recently went to the Royal Armouries and was surprised to see that they run almost daily HEMA exhibits. The sunday I went had a two handed sword display and explained the history, the attempts at recreation from combat manuals and the various styles of the time. I was thoroughly impressed. It seemed to share many principles with other weapons styles but was also great to see such a display when surrounded by armour and weapons from that time period/ I'll try to get up the video I took They explained the mortschlager (spelling?) and half swording as well as italian "flower of combat" style and some other style i cant remember. there was also an explanation on different types of guards and such. Was really awesome stuff.
I visited the Royal Armouries a while back, when my friend lived over in Leeds. I had a great afternoon, saw a longbow demo and finished it with watching some jousting. It's well worth the visit if you're interested in weapons of all shapes and sizes.