I'm assuming, if you need the technical inspection, then the car must have been more then 4 years old.

All insurance company should have a person in charge to estimate a car worth. I would advice you to go to their office and discuss face to face. Phone doesn't work that well here.

For technical inspection,it is just an inspection for the car and no requirement for a valid insurance. And also the technical inspection is valid up till 1 month after the inspection date.

So logic would suggest, that once you have passed the technical inspection, then you can renew your insurance.