There are many garage doors that do not need much headroom but you can also think a bit laterally about it too.
When you have limited headroom inside your garage or even maybe a sloping down roof which gets lower towards the back then of course you have to think about the garage door carefully. Premium garage door manufacturers these days will produce a purpose made range for their door models so the width and height need not be a problem to maximise the dimensions. Choose your preferred door type and then work backwards to see what you may end up with in your drive through height and width which is probably the most important dimensions if you intend to use the garage for a vehicle.
The average one piece up and over garage door doesn’t need much headroom at all, maybe 2-3 inches at the most (50-75 mm) nut if a remote control electric operator is required then the real problem as it is with many tracked doors is the length of the electric operator boom. Most electric motors for tracked garage doors will be at least 3 metres long as a minimum and of course are the highest point above the door so if you do have any internal lintels or other obstructions you do need to make sure you get your measurements correct.
Many people want roller garage doors, manual or electric operated, and if you look at most roller doors the average headroom required is stated as about 300 mm, and what is important here is not to get obsessed with this dimension. There are roller garage doors with less headroom requirements, but be aware this is always a bit of a compromise as the smaller roll is achieved by using thinner door slats, less strength, security and insulation. For the industry standard os about 300 mm bear in mind if you don’t have this headroom all that it will mean is the total height available will leave you a drive through height of this measurement less the 300 mm and a bit more for the bottom slat hang down. So, in effect, you can have a roller door whatever the headroom is available and all you have to be aware of is the final drive through height when open, and maybe a fascia or full hood cover to cloak off the roll that may show beneath the lintel. All not a problem though unless your height is a critical required measurement. For sectional garage doors the same principal applies and although you can get low headroom options for most models which simply gives a tighter curve to the tracking, it will mean some headroom is lost when open fully as the physics of it kicks in.