1998 saab 9.3 has just started overheating. no obvious leaks. the coolant system reseviour is boiling hot water

The classic cause of this is a head gasket leak to the coolant jacket, which will cause quick overheating.

You may see white bubbles in the coolant like dry ice, if you start the car from cold, allow the temp gauge needle to just move off the stop, then remove the radiator cap by grasping it through a large towel spread wide on top. Look then down the radiator neck while the engine runs and warms up.

There is a simple test for combustion gases in the coolant, which your local mechanic can do.

https://www.youtube.com/watch?v=a3J00_e7fyo

Just this past summer I saw this same problem on an Oldsmobile. Turned out that there was a small leak in the manifold gasket and there was air trapped in the radiator or engine block. With the car cooled off- Open the radiator plug and the radiator cap and turn on the engine and let it drain completely. When you see no more water coming out turn the engine off quickly- close the drain plug and with the car turned on- begin to refill with coolant or water while the engine is running. This should help your blow back situation but you still may have that little gasket leak from your manifold gasket. You can probably just brush a bit of Mr. Gasket ( little brown bottle) glue into the gapped area of the gasket where it is leaking from and just let it dry for about 1 hour. This can help that tiny manifold leak.

It's also possible the cooling fan isn't operating. When the engine is hot enough to boil your coolant the fan should be running. It's typically on the front side or backside of the radiator. Also, if your engine temp gauge on the dashboard is reading extremely high, you need to turn off the vehicle. Your will only cause greater damage the vehicle by letting run that hot, irreversible damage.