The strong figures from Edinburgh, Glasgow and Aberdeen come hard on the heels of the announcement earlier this week that the troubled Prestwick Airport is to be taken into public ownership to avoid the "devastating blow" its closure would cause to the local and wider economy.
The announcement from the Scottish Government was triggered by the failure of Prestwick Airport's New Zealand-based owner, Infratil, to find a buyer after putting the South Ayrshire aviation hub up for sale about 18 months ago.
Edinburgh Airport said yesterday that 958,944 passengers had travelled through its doors in September - a rise of 9% on the same month of last year.
The airport, which was bought by Global Infrastructure Partners last year, declared that it had enjoyed its strongest-ever quarter, with more than three million passengers across July, August and September.
Domestic passenger numbers at Edinburgh Airport in September were up by 8.5% year-on-year at 429,738. And there was a 9.3% year-on-year rise in international passengers to 529,206 last month.
Gordon Dewar, chief executive of Edinburgh Airport, said: "Since May, we've experienced more passengers travelling through Edinburgh Airport than ever before. This has been our most successful summer on record, with September being no exception."
He added: "We've had a massive growth this summer, having also just reported our strongest quarter on record."
Glasgow Airport, part of the Heathrow Airport Holdings operation known formerly as BAA, said yesterday that about 765,000 passengers had travelled through its doors in September. This was up 3.8% on the figure for September last year.
The Liberal Democrats' autumn conference in Glasgow was cited as one factor which had contributed to strong demand for domestic services.
Glasgow Airport recorded a 5.5% year-on-year rise in domestic passengers. It achieved a 2.6% year-on-year increase in September in international passenger traffic.
The airport also cited a "positive start" to October.
Amanda McMillan, managing director of Glasgow Airport, highlighted the fact that this weekend would be its busiest of the year.
She added that more than 110,000 people were expected to pass through the airport's doors this weekend for the start of the October school holiday week, which would "mark the end of the busy peak season".
She added: "Our attention will then turn to progressing our £17 million investment plans which will see large parts of the terminal undergo a major makeover ahead of the 2014 Commonwealth Games. It really is an exciting time for Glasgow Airport."
Ms McMillan also declared that the city could look forward to attracting "even more large-scale events" with the SSE Hydro venue now open.
A spokesman for Glasgow Airport said: "When the city does well, the airport does well. It is great to see they have added another world-class venue."
Glasgow Airport has about 30 airlines serving more than 100 destinations, including Canada, the US, the Caribbean, Europe, North Africa and the Persian Gulf. The airport describes itself as "Scotland's largest charter hub".
Edinburgh Airport has more than 40 airlines, serving more than 100 destinations.
Aberdeen Airport, which is also part of the Heathrow Airport Holdings operation, reported yesterday that nearly 322,000 people had passed through its doors in September, a rise of 6.3% on the same month of last year.
The Offshore Europe conference was cited by Carol Benzie, the newly-appointed managing director of Aberdeen Airport, as one factor which boosted passenger numbers.
The Glasgow Airport spokesman said yesterday that it was making no comment on the Prestwick situation "at this stage".
Mr Dewar said earlier this week: "It is important for passengers travelling to and from Scotland that, whatever the Scottish Government's plans, a truly competitive, level playing field exists in our airport market."