A scene from the Middle Ages
Medievalism was a term to describe concepts, practices, or thoughts which originated in the Middle Ages on the planet Earth. These terms also apply to the equivalent period of an alien culture's development as well. Such a culture would be rated a B on the industrial scale. (TOS: "Spock's Brain")
Dr. Leonard McCoy, upon observing 20th century medical practices, in particular the treatments of chemotherapy and fundoscopic examination, stated that he was "dealing with medievalism." (Star Trek IV: The Voyage Home)
In 2153, Tarquin gave Hoshi Sato a book written in a language that had been dead for over a thousand years. Upon translating it, Hoshi noted, "It's an interesting language, reminds me of Medieval Klingon." (ENT: "Exile")
During a confrontation between John Frederick Paxton and Charles Tucker, in early 2155, Paxton compared Tucker's relationship with T'Pol to be like the one between Romeo and Juliet, "the two star-crossed lovers," stating, "I can't help but wonder whether your little drama will end happier than that famous double suicide in a medieval tomb." (ENT: "Demons")
While facing the reality that Spock might die under his care, in 2270, the frustrated Dr. McCoy stated, "What's the use of being a doctor, anyway? We're only as good as our drugs and technology make us. Underneath all the tricks, I might as well be practicing in the Middle Ages." As a show of his support, Kirk chimed in, stating, "If you really believed that, Bones, you wouldn't still be a doctor after 25 years." (TAS: "The Pirates of Orion")
In 2369, the crew of Deep Space 9 encountered a medieval fairy tale character named Rumpelstiltskin. (DS9: "If Wishes Were Horses")
Prior to a racquetball game between Miles O'Brien and Julian Bashir, in 2370, Keiko O'Brien gave her husband a silk handkerchief that was decorated with a medieval Japanese design scented with her perfume as a token of good luck. (DS9: "Rivals")
While researching various species concepts on suicide, in 2372, Kathryn Janeway discussed with Tuvok the "double effect principle" on assisted suicide, a concept that relates to the relief of suffering, which dated back to the Bolian Middle Ages. (VOY: "Death Wish")
In 2374, The Doctor commented that Tom Paris' holographic 1969 Chevy Camaro possessed "medieval safety constraints", i.e. seat belts. (VOY: "Vis à Vis")
The Middle Ages are currently considered to have lasted from approximately the 5th century to the 15th century, although as evidenced by this page some people, maybe comparatively, thought of practices up until the 20th century as medieval.