Substitute Kevin Ellison found space down the left and his cross was met by Andrew Fleming, but Young palmed it away before saving from Izak Reid just moments later with only five minutes left on the clock.
The goalless draw means Aldershot's winless run is extended to five league games, as Morecambe improved from their 4-0 thumping by Fleetwood last time out.
Craig Reid fired just wide in the ninth minute after getting in behind the Morecambe defence, while Aaron Morris shot narrowly over after 16 minutes with the home side on top early on.
The Shots should have gone ahead in the 38th minute but Reid shot straight at Morecambe stopper Barry Roche after Adam Mekki's clever pass. Aldershot almost broke the deadlock after 63 minutes, Mekki forcing Roche into a fine save down to his right.
With six minutes remaining the hosts nearly bundled their way ahead following Anthony Tonkin's corner, but Morecambe were denied at the death by Young.