Talking about English, German and French romanticism.
Romanticism started with someone like Rousseau who wrote Discourse on the Arts and Sciences (1750), "which argued that the arts and sciences corrupt human morality." (Wikipedia).
Romanticists had some fascination for many forms of supernaturalism, idealized nature, and emphasized the passions over reason.
One representative example is the poet William Blake, with his poems such as And did those feet in ancient time or “Introduction” to Songs of Innocence.
Heard about "Naturphilosophie", defined as the "romantic science of nature" (by philosopher Gilles Marmasse), but it seemingly has been criticized for being speculative and bogus. According to French Wikipedia, "It is based on an organic and dynamic vision of the world, thus presenting itself as an alternative to the atomistic and mechanistic vision of modern science." That, I call being anti-science.
"Naturphilosophie" is to be found in many romantic writings: Goethe, Novalis, Schelling and Hegel (again according to Marmasse, as cited by the French Wikipedia).
Additionnally, the SEP states that for romantics, everything about life is concerned by beauty:
The most characteristic romantic commitment is to the idea that the character of art and beauty and of our engagement with them should shape all aspects of human life. Being fundamental to human existence, beauty and art should be a central ingredient not only in a philosophical or artistic life, but also in the lives of ordinary men and women.
One common concern strikingly unifies otherwise different romantic contributions. Early and late, German, British and French, the romantics advocated what may legitimately be called “the primacy of the aesthetic”. In romanticism, the “aesthetic”—most broadly that which concerns beauty and art—is not just one aspect of human life or one branch of the humanistic studies. Rather, if the romantic ideal is to materialize, aesthetics should permeate and shape human life. Friedrich Schlegel, one of the leading figures in Early German Romanticism, put this idea in a few memorable phrases: “The Romantic imperative demands [that] all nature and science should become art [and] art should become nature and science” (FLP: #586); “poetry and philosophy should be united” (CF: #115), and “life and society [should be made] poetic” (AF: #16).
Circumscribing the observation and understanding of reality under a requirement of aesthetics, is to me anti-science.
The French Wikipedia on Early romanticism states:
This will to renew the vision of the world of their time by fragments, by mixing multiple disciplines, by making cohabit metaphysics and mysticism, popular tale and poetic form, makes the first German romantics the recognized predecessors of the surrealists.
If mixing metaphysics and mysticism, and other disciplines, is not anti-reason and anti-science, I don't know what it is.
Does romanticism tend towards anti-science and anti-technology?
Science: knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method. (Merriam-Webster)
Scientific method: principles and procedures for the systematic pursuit of knowledge involving the recognition and formulation of a problem, the collection of data through observation and experiment, and the formulation and testing of hypotheses. (Merriam-Webster)
Technology: the application of scientific knowledge to the practical aims of human life or, as it is sometimes phrased, to the change and manipulation of the human environment. (Britannica)