When the draw was first made, the Silkmen were paired with the winner of the fifth round tie between Coalville and National League North side Bishop's Stortford.
Having seen the fixture twice postponed due to adverse weather conditions, the game was finally played on Tuesday night, with the Ravens running out impressive 3-0 winners on the road.
In doing so, they became the first team from Leicestershire to qualify for the last eight stage of the FA Trophy.
Macclesfield, meanwhile, moved to within two games of a trip to Wembley earlier this month as quickfire goals from Lewis Fensome and Sam Heathcote helped them advance in the competition with a 2-0 win over National League South side Hampton & Richmond.
The quarter-final tie will take place on Saturday 9 March, with winners receiving £7,500 and losers £2,000.
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