I agree with either setting it to silent or turning it off, and letting it go to VM. Personally I think it's rather rude to constantly call someone when they're on vacation. Especially when it would cost them, as even if the callee wasn't in another country, some companies will charge more when you're roaming. I'm sure he misses you, but he's not really giving you a chance to miss him, is he?
I went on a trip to visit a friend about 4 years ago, as we hadn't seen each other for years since we live on opposite ends of the country. My first day there another friend called and I told him "Hey I'm on vacation for the next few days, but DH is home, will talk to you when I get back!" He said okay...and then called me several times for the rest of the time I was there. I just ignored it and deleted the increasingly whiny and pouty voicemails, wanting to know why I wouldn't call him back, why wasn't DH answering or returning his calls? (turns out he was pestering dh as much as he was pestering me)
When I got back to the East Coast, we gave the guy the cut direct for a few months.