LJoy: " Or was that a thing only really begun by the Romantics?"
No, apart from Petrarca, there were many other "notable poets" in Italy. Actually almost all madrigals were based on high quality poetry. One particular popular poet was Guarini, of whose "Il Pastor fido" many musical settings were made, even by Heinrich Schütz:
https://www.cpdl.org/wiki/index.php/Il_pastor_fido.
In France, a well known court poet was Clement Marot, who even contributed psalm paraphrases to the Genevan Psalter, and these were set by more than a dozen composers like Sweelinck, de l'Estocart etc.
In Germany, the Reformation demanded vernacular poems for hymns, and there were a number of notable poets, among which the best known is Paul Gerhard.
In England, Elizabethan poetry was very often set to music. Well known poets are Spencer (spelled "Spenser" on CPDL), Marlowe and Shakespeare.
There is simply tooooo much stuff to single out something particular from this treasure.