A total of 513 people walked through portable metal detectors in Central Station at the weekend during the latest phase of Operation Shield.
Operation Shield visited Central Station for the first time
British Transport Police said a 15-year-old boy was found with an extendable metal baton.
A 33-year-old man was found with drugs believed to be heroin.
The portable metal detectors are similar to those used at airports and are designed to prevent knife carrying on trains and in railway stations.
Chief Inspector Iain Miller said: "The weekend's operation was extremely well received by members of the travelling public.
"The force will continue to roll out Operation Shield across the country to reassure rail users and staff that carrying weapons will not be tolerated."
The 15-year-old boy will be reported to the Children's Panel and the 33-year-old man will be reported to the procurator fiscal.
The scanners have already been used in Largs and Paisley.