Another approach is to leave something to distract your pet. Kong toys make good distractions. Kongs are hollow rubber cone-shaped toys. You can fill the center with kibble or cheese. It takes the dog awhile to get to the treat, and meanwhile they are distracted from their separation anxiety.
Crate training is another good option.
I used to crate my dog Maxie when I first moved to an apartment with new roommates. Even though she'd shown destructive behavior only when she was younger, I had nightmares about her getting into one of my roommate's rooms and eating a new stethoscope or goose-down comforter. So until my roommates and I felt comfortable with Maxie loose in the house by herself, the crate was her home while we were away. Finally the day came where we let her roam free while we were gone. I was a bit anxious myself while we were away that day, hoping that when we came back from vet school there wouldn't be a disaster.