Ryanair said it had completed a one-hour "verification flight" up to 41,000ft in Scottish airspace this morning.
The aircraft took off from Glasgow Prestwick, flew to Inverness, on to Aberdeen and down to Edinburgh.
In a statement, a spokeswoman for the airline said: "There was no visible volcanic ash cloud or any other presence of volcanic ash and the post-flight inspection revealed no evidence of volcanic ash on the airframe, wings or engines.
"The absence of any volcanic ash in the atmosphere supports Ryanair's stated view that there is no safety threat to aircraft in this mythical 'red zone', which is another misguided invention by the UK Met Office and the CAA (Civil Aviation Authority).
"Ryanair has also received written confirmation from both its airframe and engine manufacturers that it is safe to operate in these so-called 'red zones' and, in any event, Ryanair's verification flight this morning also confirms that the 'red zone' over Scotland is non-existent."
Ryanair said it had renewed its calls on both the CAA in the UK and the Irish Aviation Authority to reopen airspace over Scotland and allow airlines to operate flights safely after the verification flight.
Loganair said it hoped to operate some flights this afternoon.
A Loganair spokesman said: "Although much progress has been made since last April's airspace closures, as a result of which we are now able to operate flights safely in areas where low or medium densities of volcanic ash are present, safety considerations still preclude the operation of flights in any area where high densities of ash are carried in the air.
"The progress of the high-density ash cloud is being charted by the UK Met Office, air traffic control authorities and the Civil Aviation Authority.
"We have cancelled all flights, excluding Orkney inter-island services, which remain operational, up to 1pm today but will recommence services on a number of routes this afternoon.
"We expect to be unable to operate services to or from Glasgow, Edinburgh and Dundee this afternoon due to the presence of high- density ash clouds either at those airports or on our flight planned routes to and from them. These services have thus been cancelled."
The Loganair services which are expected to resume include, from 4pm, the service between Aberdeen and Kirkwall, and from 3pm flights between Aberdeen and Sumburgh.