Gabriel Rasmus, 28, of Stratford Road, Small Heath, Anas Abdalla, 26, of Fox Hollies Road, Acocks Green, and Mahamuud Diini, 25, of Coventry Road, Small Heath were arrested on 3 April.
At Westminster Magistrates' Court, they denied committing acts of terrorism.
They were remanded in custody and are due before the Old Bailey on 14 May.
They are accused of trying to smuggle themselves out of the UK in a lorry.
Two other men, arrested at the same time, are no longer suspected of terrorism offences, West Midlands Police said.
They have been handed to immigration authorities.
One, the driver of the lorry, has been charged with an offence under the Immigration Act.
Three Birmingham men accused of attempting to smuggle themselves out of the UK to join Islamic State in Syria have appeared in court.