Chances were rare in a low-quality match affected by the swirling wind, while both goalkeeper were also well protected by the defences.
Marc Laird had the best chance to break the deadlock when he headed over from close range early in the second half while Morecambe’s best effort fell to Jack Redshaw but his volley was straight at goalkeeper Owain Fon Williams.
The first half was a dour affair. The best opportunity came in injury time when Kevin Ellison latched on to a long ball but saw his lob fall the wrong side of the right-hand post.
Shortly afterwards, Alan Goodall saw a shot from the edge of the box deflected just over the crossbar.
Jamie Devitt curled a free-kick inches over before Tranmere striker Cole Stockton fired two long-range efforts wide of the target.
Stockton went close again late in the game after Ellison had missed his kick after being set up by Redshaw.