One way to safely get lost is to go bushwhacking in an area safely bounded by roads. I wouldn't make it too big. Maybe a half mile in each direction. Bring a friend with a GPS with you.

One way to do it is to navigate to a point about 1/2 mile away. Say 270/2500 feet. Do it using only a compass one time. Come back using just a map.

This isn't something I'd do as the first experiment.

One thing I do is navigate to a point with a just a compass to a point about a half mile away in the desert, hide an Altoid can with $10 in it under a bush, then navigate back. Sometime later, I'll go out and find the Altoid can. The $10 seems to give the same sort of fears that being lost does.

If you are interested, I could put a draft copy of a book I'm writing on advanced compass navigaton on Amazon in paperback format. It wouldn't too expensive. This is a form of compass navigation which is extremely accurate and isn't published anywhere else I know of. With practice, I've gotten so I can navigate compass only within 1% of the distance traveled which is about 50 feet error per mile. It's real slow, but it's a lot of fun.