I've always used a GSM phone as they've been available in Europe as long as I can remember. The problem isn't as much about coverage as it is about the roaming charges. Even here in Singapore (where I live and thus do not use roaming) the roaming charges are awful. I'm sure it gets worse as you head into far-away tourist spots.
A satphone at $1/min would be a miracle worker in this case.

Scott mentioned Iridium as the best bet here so I am going to look into their offer.
BTW, is there a noticeable and annoying lag when using these phones?