If you use Verizon or AT&T, you need to set your phone on airplane mode if you don't want to get dinged for incoming calls (set to airplane mode and then turn on WiFi). Or, as an alternative, forward all calls to voicemail so they never hit your phone.
That's the approach I had to use in the "old days" of using a phone overseas. I'd get a notice that I had a voicemail, which didn't start the clock running on charges (but I'm not sure if that's true for Verizon ot AT&T). I'd then use a telephone calling card and a pay phone to check messages. Or, I'd pop in a SIM card from a local phone company. These days, I'd use WiFi.
I don't do any of that any more, however, because T-Mobile doesn't punish me for using my phone when out of the country. It costs, but not at the rates changed by the other cell companies. It is such a luxury to use my phone basically like I do it at home and simply not worry about the cost, which is negligible.