I used an el-cheapo Sony Android phone ($100) on Boost running Memory Map's free 1:250,000 maps (ie 4cm = 10km) for a while, no problems tracking where I was when I had no phone signal and the GPS turned on. I'd preload the maps on the wifi network at home, or when I had data coverage.
I've now swapped to a Google Nexus Tablet that I got for $120 or earlier in the year, and still run Memory Maps on it. I just download the maps that I need before I head out, and off I go. If I need more maps I download them via my mobile phone as a hot spot.
In terms of dedicated GPS units, I used to be able to get the GPX tracks out of my Garmin Nuvi onto their software, and then I could save them. It was a bit of a time consuming process, but it worked well, and I could save my waypoints from Memory Map onto the computer and then upload them into my Nuvi. The caveat there is that the Nuvi was about a 2008 or so model, so the tech might have changed a bit now as there is the move towards virtual licences rather than the DVD based maps I had.