In my world the concept of Science and Magic works in two different ways. They can either be two separate things or they can intertwine. I have my concept with science such as human technology and advances and I have my concept for magic being your standard mythical creatures, witchcraft and basic Fairy Tail magic that's a little more advanced, but I really want to figure out a way to intertwine the two concepts so what are some tips I can do to have science and Magic intertwine each other ?
Try to turn magic into a science?
What kind of magic is it? If I know then I can help more
So there's the theory that all magic is just tech we don't understand yet. Maybe learning magic winds up being an extensive chemistry lesson (like witches spells) or a lesson in quantum physics (like fairy magic). Perhaps its part of a biology we don't have the science to understand (like non-sentient creatures who wield magic).
Or, think about things like how science allows us new methods of manufacturing and refining. Perhaps a material, like a gem or a metal, has a magical property, and you could build tech from that material. Like, instead of a regular quartz-and-silver watch, it's a magic metal-and-magic gem watch, that tells the time, but has settings for going back and forward in time. A tech piece, but with magic from the materials.
Or, discovering new ways to make our magic stronger as we solve science and tech problems. Trying to get a rocket to the moon? Helped us solve the gravity equation, and now brooms can fly. Trying to cure mental illness? We figured out how the mind works enough to learn magical hypnosis and mind reading. Discovered a new element by particle collision? It's also the element that helps us manipulate matter, allowing shape-shifting magic to become a controllable power.
Just some thoughts :)