Offshore navigators use celestial navigation as a backup for the GPS. Use a sextant for taking the altitude of a celestial body and OpenCPN to plot the celestial circle of position instead the LoP -Line of Position-. Repeat this and take at least three sights. You easily can check if any danger is near your fix, and the uncertainty in your position.
Free software to create the GPX file that serves as an input to OpenCPN from sextant observations is available at http://sites.google.com/site/navigationalalgorithms/ (The Running Fix problem is easily solved using CelestialFix.exe)
Chart Work - Traditional paper chart work on an ECS.
Parameters of a circle of position in astronavigation.
Circles of position or Circles of equal altitude. General scale.
Fix and confidence ellipse. Coastal scale.