A system for motoring a gas turbine engine of an aircraft is provided. The system includes an air turbine starter operable to drive rotation of a starting spool of the gas turbine engine and a starter air valve operable to deliver compressed air to the air turbine starter in response to the starter air valve being open. The system also includes a metered orifice coupled in a bypass configuration around the starter air valve to deliver a reduced amount of the compressed air to the air turbine starter while the starter air valve is closed. The reduced amount of the compressed air delivered to the air turbine starter limits a motoring speed of the gas turbine engine below a resonance speed of the starting spool of the gas turbine engine.