Matthew Hamshaw had the first chance for Macclesfield with a shot from 10 yards which was blocked by Garry Richards. Fellow forward George Donnelly was then thwarted in the box by the hard-working Andy Frampton.
Gillingham came back and striker Danny Kedwell robbed Carl Tremarco on the right flank before arrowing a shot toward the top corner which forced a flying save from Veiga.
At the other end, Sean Brisley forced Frampton to clear off the line with a powerful header.
Veiga came to Macclesfield’s rescue again four minutes after the break when he palmed away a fierce volley from Curtis Weston.
Veiga was tested again moments later when Danny Jackman unleashed a drive from the edge of the box that the keeper tipped wide.