Edinburgh saw 794,792 passengers for the month, a year-on-year increase of 12.4%, and its 'busiest November ever'.
Glasgow's monthly figure of 618,583 was a rise of 7.7% on November 2014.
The figures suggest Edinburgh Airport will have its busiest year on record in 2015, while Glasgow Airport will be busier than in any year since 2008.
International traffic has been especially strong at Edinburgh, with annual growth of 22.5%.
Qatar Airways has expanded its service to Doha, and numbers are reported to be up on routes operated by easyJet, Ryanair, Etihad and Turkish Airlines.
Edinburgh Airport Chief Executive Gordon Dewar said: "These exceptionally strong figures represent our busiest-ever November; Edinburgh Airport has experienced passenger numbers levels in November - a quiet month in air travel - on a par with what many other regional airports do at the peak of summer.
"This tremendous achievement is a direct result of our commitment to increasing connectivity and choice and improving the passenger experience.
"This has been another record-breaking month and is a sure sign of the growing success of both Scotland and Edinburgh as a destination which emphasises our position as a key driver for Scotland's economic growth."
Glasgow's international traffic was up 12.2%, with new services to Budapest, Vilnius, Lublin and Berlin.
Domestic services have also expanded, with a new route to Exeter and extra capacity on flights to Gatwick and Stansted.
Glasgow's managing director Amanda McMillan said: "2015 has been a fantastic year in terms of passenger growth. Our November figures not only guarantee we will end the year on a high, they will ensure we are in a strong position as we prepare to enter 2016, the airport's 50th anniversary year.
"In addition to gearing up for the Christmas getaway, we have already seen a new service to Milan launch this month with easyJet and there is more to come before the end of the year.
"Later this month Blue Air and Wizz Air will both begin a new service to the Romanian capital of Bucharest and British Airways will start a new Saturday service to Salzburg for the ski season."
Passenger numbers grew significantly in November at Scottish airports, with the introduction of new international services.