I had a cheap pedometer once. It was not very accurate and failed to record all my steps. It could also get jiggled and record a step twice. Steps vary in length when going up or down hill, so even if you had a pedometer that counted all your steps, it wouldn't convert steps into miles accurately. I prefer to count miles instead of steps.
Way back when I hiked all summer, my hiking was done in Wilderness Areas of Montana. These mountain trails were marked with mile markers and calculated with a "tally whacker", a device consisting of a bicycle wheel mounted with a long handle that an employee pushed ahead as he walked. It counted revolutions and was calibrated against a known mile that was actually measured manually. It was about as accurate as a device could be. Now with a GPS that actually records your path with all the twists and turns (some are better than others), you might be able to use that, but I'm not sure of it's accuracy, because I think they read the path every few seconds or so, which might short cut things like switch backs and other abrupt turns, but I'd speculate that it would still be more accurate than a pedometer.
I eventually got rid of my compass for hunting and found my way only with a GPS. I could set the location of my truck, wander about wherever I wanted and then walk directly back to the truck. This was a life saver when I would park at the end of the road. With a compass, I could walk in a general direction but then miss the end of the road, and then have no idea which direction to go when I realized I didn't know where I was. A GPS that also includes a map would be very helpful, but my cheap one only allowed me to enter way points. At any rate, a GPS is one handy piece of equipment.