OP, how does your anxiety generally manifest itself? What sort of things bother you day-to-day? Is this about trusting him, or is it about lack of control by not being able to contact him when his phone is off? Is it about being home alone, and afraid of that at nighttime? Or feeling looking after your children on your own is a challenge or too much responsibility?
My partner sometimes has to travel for work and I dread it. It bothers me for weeks beforehand. I feel stressed and quite down. It doesn't affect my appetite or sleep, but I often get mouth ulcers (which in me, are a symptom of stress). For me, the issue is being home alone at night. I don't miss his company or want his attention, so much as I struggle to feel safe without another adult in the house. I feel this way because a previous house was burgled once (I was the one that found it and had to watch the place being dusted), and because when I was in my teens and on holiday with friends, we were alseep one night and broken into by two drunk/high older guys. I thought it was a rape/murder type of situation. It was incredibly traumatic and has obviously left me with a degree of PTSD.
DH knows this, so he limits his travel where he can. We always make sure our security alarm is working and I arm it at night. We go through household security, and I stay up late so that I am tired enough to fall straight to sleep when I get into bed, rather that lying there in the dark freaking myself out with every household noise I can hear.
This is my problem, and because DH and I are a team, he tries to help out by being at home as much as possible, but I also need to be supportive of him on the rare occasion that he has to travel. And, each time he goes, although it's stressful, I actually feel a little bit proud of myself for "surviving", and the stress I feel before his next trip is less and less each time. It's like exposure therapy. I have to confront the issue in order to get over it. He's recently got back from an overseas trip, and has the opportunity for another very soon. It's in no way necessary and he could decline it without anyone batting an eyelid, but I am encouraging him to go because it is good for him and good for me.
So, I guess my point is this: If your issue is your personal anxieties, rather than his phone being off or your trust in him, then the best thing you can do is let him go with outwardly good grace, get through it, and then feel proud of yourself for having coped. Avoiding things that cause anxiety only make the anxiety worse. I'm saying this as an obsessive-compulsive who has done CBT, and as a clinical psychology graduate, so I get how you're feeling and don't judge you for it.