Bring back heresy trials!
For over a millennium the Christian church's doctrine claimed the Sun orbits the Earth, based on faith. Those who would dare to disagree would face torture, a heresy trial and being burned at the stake.
Eventually in the Renaissance period, Galileo was one of those who suspected this geocentrism idea was incorrect, and that the Earth actually orbits the Sun. Heliocentrism. He tried to use evidence of non-geocentrism, using observation of Jupiter's moons viewed through an early telescope. If non-geocentrism could be established, then heliocentrism is a possibility, but would need further research. Of course, considering potential outcomes of such research would need freedom of belief...
"Freedom of belief is pernicious. It is nothing but the freedom to be wrong." -Cardinal Bellarmine
Galileo argued in favour of experiments to learn more:
"The doctrine of the movements of the earth and the fixity of the sun is condemned on the ground that the Scriptures speak in many places of the sun moving and the earth standing still... I think that in the discussion of natural problems we ought to begin not with the Scriptures, but with experiments and demonstrations."
The church was having none of it, and made a formal declaration in its indictment of Galileo:
"The doctrine that the earth is neither the centre of the universe nor immovable, but moves even with a daily rotation, is absurd, and both psychologically and theologically false, and at the least an error of faith."
Cardinal Bellarmine, during the trial of Galileo, stated:
"To assert that the earth revolves around the sun is as erroneous as to claim that Jesus was not born of a virgin."
Of course, he may have been correct there...
Thereby the church tried to stifle any use of evidence to investigate further, in case it produced results that conflicted with its doctrine. Galileo was tried for heresy in 1633, and shown the equipment that would be used to torture him if he didn't recant. He recanted, had to end his science, and died a broken man.
http://www.law.umkc.edu/faculty/projects/ftrials/galileo/galileoaccount.html
The same church finally accepted Galileo had been right - in 1992.
However, Galileo's work did inspire others who were able to repeat his observations and take them further, outside the control of the church (this was the time of the Reformation). This is regarded as the end of the scientific Dark Ages, which began in 415 CE when the secular pagan scientist Hypatia was murdered by a Christian mob in Alexandria.
http://penelope.uchicago.edu/~grout/encyclopaedia_romana/greece/paganism/hypatia.html
If scientists received torture and execution instead of Nobel Prizes, then the church would be able to stop such scientific discoveries that make them keep having to change their stance. It worked for a thousand years, so it could work again.