If your classic car steering wobbles, first check the condition of the wheels and tyres. They may be slightly distorted. Replace the tyres if they’re old irrespective of tread depth. Jack the car up and spin the wheels. Use a fixed marker to assess if the rims are distorted. If not, see if the tyre treads twitch or wander as the wheel spins. If all seems well here, check for play in the steering or suspension joints. Have the tracking set and the wheels balanced too.