The following event happened many years ago, before cell phones were cheap and lightweight. I was hiking with a friend on a fire trail that was several miles from the nearest road - not exactly wilderness, but it was in the middle of parkland/water company land, and in a generally unoccupied area. I carried a 2-meter-band handheld radio. Even today, the area might be out of reach from the nearest cell phone tower.

We encountered someone who had broken his ankle. It wasn't an emergency/911 situation, but he really wanted to get in touch with a park ranger or staffer who had access to the road (there was a locked gate) and who could get him a ride out, as opposed to him hopping out in many hours with the makeshift crutch he had fashioned from a branch.

I was able to contact an amateur radio operator through a mountaintop repeater, and relay a message through him to the regional park police. In less than an hour someone from the water company had unlocked the gate and he was on his way out with a ride courtesy of the park police.

Conclusions:

1) As others have mentioned, having the frequencies and PL tones of likely repeaters in the area was crucial.

2) Also important was carrying the phone numbers of the relevant emergency agencies. The person I reached wouldn't have known who to call - he was far away. The fact that I could say, "please call this number, and tell them..." was a big time saver.

3) Describing where we were was a problem. It was an awkward relay situation - I'd tell the other ham, he would speak on the phone, the dispatcher would ask a question, he would relay it back. Even though he had a phone patch (which in theory allows direct conversion between radio and telephone) it was _not_ working well and he ended up having to relay. Furthermore, I had a hiking map of the area, which gave the name of the trail we were on, but this name did not match up with any name on the dispatcher's map - so I had to describe where we were by starting at a common landmark and then giving info about our route. We went back and forth multiple times. The more maps the better - maybe if I also had a quad map in addition to the trail map, I could have more efficiently explained where we were.