Most dogs will take to a cage like a duck to water, and merrily snooze in there while you go out once they're confident and comfortable with the new device. I have a pet food shop (but do not sell cages) and have experienced this many, many times. What trainers like Wendy forget is that they only see the ones who have already tried and failed with cages, etc., so not the majority of cases by any means.
However, to get them happy in the cage so the separation becomes less of a problem is the tricky bit. In my case we simply bought a cage for one dog as he was very aggressive to other dogs and I needed to confine him while he was in my shop to stop him eating other customers. He simply walked straight in the first day, settled down and snoozed in it ignoring everything else ...... which I count as pure good luck. You'd assume favourite treats fed in there and only very minimal time in the cage to start with would be a good starting point.
The second cage came with a Jack Russell who I took on at 8 months. He had to continue sleeping in it in our home to stop the first dog attacking him until they were comfortable together, but he missed it when we took it away. So we left it with the door open at all times and heaped blankets on it until he got too warm one summer and I sneaked it away one afternoon. I made it less comfortable than anywhere else to get him out of it, so again I expect making it more comfortable than anywhere else would get a dog into a cage.
Finally, our Saluki has been with us 12 months now and he enjoys his cage when in our shop one day each week. He doesn't react to treats (he's very hard to feed) and can't see the point to toys or chews, so again we just put him in the cage and left him to decide for himself and he likes it very much. Nobody can bother him, he can snooze in peace and he has an array for favourite beds, blankets and cushions in there.
I've suggested to customers in my shop that they try their dog's favourite long lasting treat in the cage and make sure that treat is never fed anywhere else. Beef bones, cooked, seem favourite with filled hooves and bones second. If that hasn't worked and the dog is still worried by being left for more than ten minutes, frozen yogurt in large Kong style toys plus the bone/hoof. Having two treats tricks a dog in to being greedy - they all fear one being stolen even if they're alone. I've not had to suggest anything else so far as the second method seems to have worked for everyone if the first didn't. Maybe I'd say try leaving the dog out of doors (my two like that) or shop in the evening when it's cool and take the dog with you (what I do, simply because it's habit these days), I don't know.
Whatever you do, make sure the anxious reaction isn't because your dog thinks he's top of the pack and you're his underlings leaving him - that one must be hard to break and I wouldn't fancy tackling it without professional help.
Good luck