Good ruler supports inventing of useful things. But this question has two sides.

• own support of inventing of useful things


• prevention of false inventing

Base:

Many inventions are side-effects of searching for something else. And base of current chemistry is in alchemy and its attempts to find philosopher's stone or so. Also, there are some researches that have not direct effect but still they are needed.

Theory:

Fantasy without philosopher's stone (or so) may sound like a non-sense. But let's say that ruler does not believe in existence of philosopher's stone (or invisibility or so) and wants to invent something really useful (for example how to improve public health and cure some illnesses) instead it and is resolved to pay such research very well.

And where are money, there are also cheaters. So ruler wants to check that all researches he (or she) pays are really researches of only things related to main goal.

Background/Inspiration:

This question is inspired by one old czech movie and one concrete scene from it:

Alchemist should prepare potion of rejuvenation but he does anything else instead it (for example floor polish).

In one stage of that inventing (and in that mentioned scene) he should find mandragora and prepare it but he cooks sausages with horseradish in great pot instead it.

Historically, this is what patents are for. A patent does three main things:

FIRST a patent grants the inventor a monopoly on making and selling their invention for some period of time, with legally established methods of enforcing the monopoly. They can charge license fees, or sue to stop infringement and obtain reparations.

SECOND a patent requires the inventor to disclose the invention in public records -- which means that, in order to gain his monopoly, he has to tell the world how the item is made. Disclosure does two important things: it ensures that the invention can be copied after the patent expires, and it allows anyone to replicate the patent for research purposes, which prevents patenting bogus inventions. If your invention works, but no one can replicate it, someone else can patent the actual way you make it -- and if it doesn't, no one will want to buy it.

THIRD a patent expires after some period (in the USA, that's 17 years, with a shorter renewal available in some cases). After that, anyone can make the patented item, or make improvements on it, without paying a license fee -- the patented item becomes open to competitive forces.

Patents aren't perfect -- one could argue there are some heinous issues with current American patent law -- but historically, they're widely held to be a major contributor to scientific and industrial progress, by making inventing both profitable and publicly available.

There are two ways of achieving this:

• Supporting the research


• Rewarding for inventions

Of course, any good ruler can do both.

For research support, the ruler can (in the order of practicality in medieval times) employ scientists directly, establish an academy, give grants to an independent institution, or give private grants to any researcher.

For rewarding the inventions, the ruler should establish a scientific panel for evaluating them, and then either employ the inventor directly, or give him (or her) a grant to implement the invention independently. Patent system (@Zeiss Ikon) also can be helpful.

+1 @ZeisIkon, Patents are one arm of a two prong approach to getting a culture of invention going.

The other prong to get this going is expressed interest by the ruler. If the ruler likes painted duck decoys, people will get really good at painting duck decoys to get the ruler's attention.

If the ruler lets it be known to the land that they love new things and new ideas, people will bring new ideas to them to show off. If the ruler then does something that rewards the ones with truely useful or interesting inventions, the rest of the people will see this as a method of advancement and a way to catch the ruler's eye.

Nobles may search for clever people to present to the ruler and thus gain prestige that way.

Since the ruler cannot see every new idea, have festivals to show off new inventions. That way people without noble backing can see that they have a chance to get recognition.

Eventually there would have to be some kind of filter so regional events will have to be held with the best stuff being presented to the ruler.

Also, events can be held with a theme and/or to solve a particular problem. For example, figure out a way to provide more water to the capital or grow more food with less work. However, there still should be general events to promote creative thinking.

Those presenting their inventions at a contest can be given patents if the invention is unique and useful.

Run a peer-reviewed journal

Presumably, the king is funding research, but there's a lot of bogus science. The king probably doesn't understand alchemy, but the alchemists do. Require that everything published in the journal be verified by an independent alchemist or two. Give grants for successful publishing. The more consistently your invention works, the more money you get from the king.

Like patents, there are ways to game the system, but this at least weeds out the obvious liars.