I'm not sure which Garmin eTrex you are using, but with the eTrex H, you can get a case to put the GPS in.
On the back of the case, there is a clip, to clip the GPS to a belt, rucksack strap or something just as ideal.
Mine I clip to the chest strap of my rucksack, mainly for convenience, but I can then twist the unit sufficiently to view the screen.
I also loop the cord on the back of the Etrex H around a strap, so if I do drop the GPS, its can be pulled up easily.