Premium fuel can indeed provide the car or vehicle owner with improved or better gas mileage. However, not every car owner can benefit from using premium fuel and therefore gain an improvement in their gas mileage. Not every petrol or gas station provides premium fuel, although, in the UK, several forecourt suppliers have a branded premium fuel.
Another limitation to gaining the benefit of improved gas mileage from using premium fuel is simply that not all vehicles can give you this benefit. Generally, only larger engined cars can show an albeit small in some cases, gain in their gas mileage figures when premium fuel is used.
Those smaller engined cars and those that use 95 RON fuel or lower as specified by the manufacturer will generally show no gain in gas mileage if premium or 97 RON fuel is used. To fill your tank with premium grade fuel in these cases is simply a waste of money. It could also have the effect of making your vehicle run 'rich' as you will have created an imbalance in the air/fuel mixture.
Another gain for the larger car in using premium or 97 RON fuel is an increase in power, this in fact is where the improvement in gas mileage is found, as your car works less hard to produce similar performance to the output it shows when using 95 RON or regular fuel. This is also helpful when towing.
For the branded fuels supplied in the UK that have their grade increased to 97 RON, often an additive is also supplied within the fuel that has a cleaning/de-coking effect upon the engine. Although fuel manufacturers have many claims to the beneficial effect of such cleaning additives, they do have their sceptics and one petroleum company removed their branded fuel from the market for a while due to complaints of engine failure. However that brand has since reappeared after improvements and testing.
The best way to discover if changing to premium or RON 97 fuel would be beneficial to your car, and would show you improvements to your gas mileage figures would be to carry out a simple test. Simply record your mileage figures over a known and regularly traveled route over several tankfuls of petrol. Then, when the fuel tank is nearly empty, fill it with premium grade fuel and then cover the same distances and routes, again recording your figures. Although this is not an entirely scientific test, it should give you a fair idea if premium grade fuel is for you.