Aldershot's Danny Hylton had a penalty saved as lowly Plymouth stretched their unbeaten run to five games.
The hosts had an excellent chance to open the scoring in the first half but Pilgrims keeper Jake Cole was equal to Hylton's spot kick.
Nick Chadwick forced a good save from home custodian Ross Worner before Hylton headed just wide for the Shots.
After the break Cole saved expertly from Anthony Straker and Charlie Henry as Plymouth hung on.
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Aldershot manager Dean Holdsworth told BBC Surrey:
"We've done everything right apart from put the ball in the net.
"Missing a penalty doesn't help, but we've created a number of chances and on another day we could easily have won that game by two or three goals.
"I can't fault their effort or their desire. Man for man we were decent, but goals win games and unfortunately we didn't get any today. As much as I'm disappointed, I can't fault their efforts."
Plymouth Argyle manager Carl Fletcher told BBC Radio Devon:
"It's one of those games that we realise we weren't firing on all cylinders, but we've dug in and ground out a hard-earned point. This is the kind of game we would have lost convincingly earlier in the season.
"I'm pleased for them to come out with it with a clean sheet
"Jake Cole is in a good run of form at the moment and long may it continue."