Steven John Maloney, 58, and his 30-year-old son Ashley Richard Maloney – both from Harrogate – were caught speeding on roads between Tadcaster and Sherburn in Elmet.
They were followed by an officer riding an unmarked motorcycle at speeds of up to 110mph.
Both were found guilty of excess speed and convicted following a trial at Northallerton Magistrates’ Court yesterday.
They were both sentenced to 70 days’ disqualification from driving, and ordered to pay fines, costs and victim surcharges totalling £1,050 for the father and £1,130 for the son.
The offences took place on May 9 last year.
Traffic Constable Martin Hayes of North Yorkshire Police’s Roads Policing Group said afterwards: “The two riders in this case chose to ride at excessively high speeds and are now suffering the consequences of that choice.
“As the motorcycling season begins, this should serve as a reminder to all road users that we welcome law-abiding drivers and riders to North Yorkshire to enjoy the roads and ride responsibly.
“However, North Yorkshire Police employs a number of enforcement methods including the use of marked and unmarked cars and motorcycles along with the safety camera vans and the courts will deal robustly with any offences reported to them.”