The drivers were clocked at 95mph by members of the Lincolnshire Police ARV unit - the highest speed the two man police team had ever recorded in a 30mph zone.
The tweet said the officers "were both left speechless" by the incident.
The incident is believed to have happened late late on Thursday evening, although police have as yet been unable to provide any further details.
The tweet from the ARV account, which was posted at 12.20am on Friday, says: "So the Boston late turn were left stunned by the highest speeds recorded by this double crew in a 30mph limit. 95mph.
"We were both left speechless and both drivers of both cars will be having days in court.
"This is in no way acceptable for any reason. #arv #roadspolicing #fatal4"
Lincolnshire Police ARV Unit is a 24/7 armed response, taser & specialist roads policing, and is part of East Midlands Operational Support Service.