Iridium makes the most reliable SAT phone on the market. They run for around $1300. Most guiding companies carry SAT phones and many will even rent them out in the off-season—which is a more affordable solution than purchasing one for a trip. SAT phones are not impact or water-resistant so they should be stored in a Pelican or Otter box. I wrap mine in a bandanna and stow it in a Pelican. For longer trips, consider carrying an extra battery.
Despite what secret agent Jack Bauer can do with his SAT phone, they need to be handled with care and used outside—not three stories underground. The antenna have contact satellite(s) overhead. Once you receive a signal, get out your critical information first (nature of the emergency/injury, your location, etc...) then talk about pizza and beer for the post-trip fiesta. You may have contact for two minutes or 20 minutes, depending on your location.
For a trip to Fiji, you may want to consider augmenting your SAT phone with an ACR Personal Location Beacon and an ACR Firefly Solas Strobe Light. With this gear, you will possess three essential signaling tools for remote travel.