"I just use the squiggly lines on my map to determine the altitude."
I use the numbers rather than the lines.
Ordinary GPS receivers can give you moderately good elevation readings as long as it has a good view of the sky. When the view of the sky is very limited, there can be huge accuracy problems. Survey GPS receivers can do much better, but they cost much more money and require more time to develop the accuracy.
Barometric altimeters can give you good elevation readings as long as the weather (air pressure) is relatively constant. When a storm is coming in and you suddenly seem to rise by 500 feet, that can be a problem.
Topographic maps can give you good elevation readings, as long as you know precisely where you are on the map. So, if the GPS receiver can give you good horizontal accuracy, then that position can be placed on the printed map, and then you get Nick's position from the squiggly lines and numbers.
There is no perfect tool.