I think there a couple of preliminary points that need to be addressed. This is marked as system agnostic, and that is probably a good call in the sense that neither the question nor this answer are tied to any particular setting, but it does not apply to all settings. Some settings make it very easy to make magic feel "science-y" and others makes it nigh impossible either deliberately or just by not having things well defined.
Second, what makes something feel like science, especially in the way this question seems to be asking is being well defined, and susceptible to something akin to the scientific process, not using scientific sounding words. In fact, scientific sounding words might make things worse in terms of realism or making something feel like science. They can lead to someone with real science knowledge leaping up and saying "That's not how that works at all" (my wife gets really mad when I do that with Star Trek) or "That might work, but what about the side effects?"
Something which is predictable and can be studied experimentally feels like science.
Which brings me to the core of my answer: To make magic feel like science you let it be consistent. Shadowrun's Hermetic magic (my knowledge comes from 2e, I don't know if this has changed) felt that way to me. There was a whole background theory of mana and astral space and their interactions that felt like something a scientist could study. The results were predictable, a magic theory skill existed, and some of the fiction around it suggested that magic theorists worked a lot like scientists and used a lot of math. It felt a lot like science, though it used magi-babble instead of science babble.
In fiction, the Iron Druid Chronicles come to mind, at least in terms of druidic magic. The basics of how druidic magic are laid out in the first book of the series and never deviated from. After the first book, the druids occasionally pull out new tricks, but they always flow form the principles laid out in the first book and always feel consistent. The main character also spends a lot of time talking about how his studies of science have helped him use his magic better. Druidic magic is predictable, and can be informed by knowledge of other fields of science. This makes it feel a lot like a science.
What makes magic feel un-scientific?
It might help to look at the opposite end of it. To make magic not feel like science, you deliberately leave it vague, unpredictable, and poorly understood even by its users. It then becomes hard to study (in any conventional sense of the word study) and mysterious. It might even be a living thing with something of a mind of its own. Magic in The Last Unicorn felt magical and was certainly not scientific because of that.