I use a leather guitar strap thingee called a Neck-Up. It's a great gadget; it allows you to prop the guitar on your leg with, well, the neck up, and if you play in the classical position, i.e. sitting, it keeps you from having to prop your foot on one of those classical guitar foot-rests. These can be bad for you long term, sciatica and like that, and when you can keep both feet flat on the floor, you can use a regular chair and not have to worry about carrying your foot-rest with you. Way more comfortable, too.
Acoustic players who prop their instrument on the other leg, it works fine for that, too.
Mostly, it works great most of the time. Now and then, one of the suction cups that keep it attached to the guitar comes undone. (If you have an acoustical with an end pin, you use only one of the cups, which attaches to the waist of the guitar. If you don't have an end pin, as in a classical nylon stringer, the thing uses two suction cups.)
There are two sizes of cups, and for security, I ordered the larger ones. But even so, the strap goes slack now and then when the upper suction cup lets go. I think it has to do with the finish, which is thin on my guitar.
Not dangerous, the guitar is on your lap because you are sitting, so it doesn't go far, but it is annoying.
So, since I had a couple of extra suction cups, it occurred to me that I could upgrade the system, and I added two more of them into the mix. Two high, two low, paired large and small.
Much more secure with four instead of two. It hasn't peeled off accidentally yet.