Oh how I despise armadillos,
Yes very nocturnal and hard to get rid of. Finally got them slowed down at least in the yard and now that this has been brought up it will now be jinxed! Have taken them out with the .22 and .25 air rifle .17 HMR and .22 rimfire. Like Gavin said if you are sneaky walk right up on them. The machete works real nice, three have fell victim to that and one was a double while the Mrs. and I were loading up for a duck hunt at dark thirty. They were under the apple tree grubbing around the grass was wet and as the Mrs. held the light I went in swinging. That was a head shot and second on across the back. When we get a long freeze spell they will show up more in the daylight being hungry looking for thawed ground. The things are protected but you can protect your place from damage. So those that you see damage but not them? Find their hole or den. I kept a 120 conibar trap when I sold all my traps. For those who don't know it is the double spring version of the 110. Muskrat, and mink size. An armadillo can't get it's body through it but the trap will smash it's head .
I did some looking up about them. Hard to live trap. You can try to funnel them into a trap and i have tried and failed. A friend told me about box traps. Look that up if you want. The trap needs to be baited with armadillo poop to get them in it. Videos of it. You can buy plans for the trap, complete kits and even armadillo poop. I don't think i am ready to stoop for poop quite yet .
http://thearmadillotrap.com/buy.html
BilletHead