I think the Romans largely managed it through building level roads to march on. Most pre-industrial armies were marching off-road. I would be saying walking 2 miles/hour on a tarmac road would be someone's maximum before causing damage. Offroad I'd be saying 1.5, maybe even 1 mile/hour depending on the terrain.

In the late republic they were sustaining this pace in hostile territory -- where the roads were basically dirt winding along ridgetops and riverbeds.

Supposedly, the early US settlers (or maybe it was the conquering US army) utilized native American couriers that could run 30 miles a day like it was nothing. I've seen stats as high as 240 miles in 3 days!

I wish I had a link to the source (I'll dig it up when I have more time). I discovered this while researching "fox walking", the toe-first method of human locomotion that some believe is the natural means of human motion, before the advent of stiff-soled shoes. This skill appeared to become mostly lost in the indigenous populations after the Spanish introduced horses to the Americas.

A search on "native american" and "ultrarunning" should render some good links for those who are curious.

As an aside, as anyone who's ever read Stephen King's "The Long Walk" can attest, sustaining a 4mph walk is quite tough. I mean, who hasn't read that story and tried keeping that pace with GPS in hand?

There are Indian tribes in Mexico still running like this. Check out "Born To Run" by Christopher McDougall (excellent book by the way).