The Magpies were perhaps lucky at times to secure a point to start off with in Group D of the Europa League but will also reflect on numerous missed opportunities
The home side posed the visitors numerous problems throughout and came closest to breaking the deadlock through Valentin Roberge's header, which came off the bar, and then through Davide Santon's goal-line clearance.
Newcastle had chances of their own and hit the woodwork three times, with Shola Ameobi twice and Dan Gosling coming desperately close to sealing what would have been a smash-and-grab win.
Alan Pardew rang the changes from Monday's 2-2 draw at Everton, with in-demand striker Demba Ba left out alongside his Senegalese strike partner Papiss Cisse, who missed the trip to Portugal through illness.
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The Magpies started tentatively, with the Portuguese side coming close to establishing a stranglehold in the match as early as the second minute as David Simao's flashed cross in just eluded the desperately unlucky Heldon unable to turn it home at the far post.
Leocisio Julio Sami was proving a constant thorn in the side of the Magpies' defence and twice came close to breaking the deadlock after more wonderful play from the hosts.
First, the Guinea-Bissau striker latched on to Simao's corner and put in a hooked effort which was well dealt with by stand-in stopper Elliot before lacklustre defending from Mike Williamson let Sami away again but Elliot proved the hero once again for the visitors as he stopped with his legs.
Maritimo were still on top but after Haris Vuckic took aim with a 25-yard shot that was turned behind for a corner, a series of golden opportunities suddenly materialised for Pardew's men.
The upright was rattled twice with a matter of seconds. After a corner broke loose to Williamson, a goalmouth scramble ensued, with the big centre-back unable to turn it in from close range. The ball eventually found Ameobi, who was guilty of an even more glaring miss.
With the goal seemingly at his mercy, it appeared that Ameobi had the simplest of tasks to lash the ball home but, inexplicably, the Magpies forward decided to nod it goalwards only to watch as the ball agonisingly struck the post.
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Gabriel Obertan and Ameobi both tested the goalkeeper with low efforts but Maritimo were not about to sit down and let all their early endeavours disappear.
A nice move involving the dangerous Simao and Sami resulted in Danilo's low shot being blocked as Newcastle struggled to keep up with the classy hosts' tempo. Williamson, in particular, was finding the pace and trickery of the forward triumvirate difficult and his sloppy passback was picked up by Elliot but, unbelievably, no indirect free kick was awarded on the stroke of half-time.
Newcastle started the second period in much better fashion, but struck the woodwork yet again, Ameobi crashing a shot against the bar after strolling in from the left flank and taking a good touch.
Maritimo were stung by the close shave and soon began to monopolise possession once more as they sought to re-establish their dominance, substitute Philipe Fidelis dos Santos coming within inches of snatching the lead against the second-half's general run of play.
This time Sami rolled the ball in from the left for the onrushing Fidelis, whose low left-foot shot flew just wide with Elliot a beaten man in the visitors net. The keeper did better, though, to deny a similarly low effort from Sami shortly afterward.
A flurry of changes materialised as both managers set their teams up for the final 10 minutes but it was beginning to become desperate for both sides.
Maritimo forced a corner down the left-hand side and, when it was whipped in, Roberge's bullet header was somehow dramatically dealt with on the line via a combination of Santon and his own crossbar as the Magpies survived the best chance of the game.
Both teams tried to force the issue as the final whistle approached but for Pardew, despite being largely outplayed, this result may prove a source of frustration after some extremely near misses.