
A Certain Magical Index: This is rather rare due to the fact the science and magic sides are in a cold war at best and hate each other at worst, many on the Science side either don't know or don't believe in magic, many of the Magic side don't see the point in immersing themselves into science beyond necessity, and that in most cases magic and esper powers are incompatible for the same person to use.rocket-propelled lance, Precision Guided Chakrams, ect.
It is established early on that the rules for Buso Renkin is take an ordinary weapon, the lower-tech the better, and give it a magic power, i.e.
Opposing FMA, Buso Renkin uses Alchemy as basically a synonym for Magitek. The lead character is unique in that he can't use that magic, thus rendering even personal vehicles unusable to him. Broken Blade features a world where any form of technology more complex than a hand tool involves the use of magic to manipulate quartz. But the fact that subsequent Gundam stories have continued to use the concept even after all the major psychic research was proved to be flawed or outright fraudulent places them firmly in Magitek territory. Even the original Mobile Suit Gundam, paragon of Real Robot-ness, has it in the form of Psycommu weapons, though this may not technically qualify, as at the time it was made, many serious scientists were conducting research into Psychic Powers. Often shows up in works by Yoshiyuki Tomino, most obviously Aura Battler Dunbine. In The Ancient Magus' Bride, this is the product of Magus Craft, which uses magical power as a power-source rather than electricity. In Ah! My Goddess, the magical system underlying existence is likened to computer code, and manipulated accordingly. Courtesy of Ted Woolsey's translations, this fantastic science and the inventions using it became known under the blanket term "Magitek." The Trope Namer is Final Fantasy VI, where the Gestahlian Empire had suits of Power Armor, dozens of Humongous Mecha, and fleets of flying Mini Mecha, armed with various lasers and missiles powered by the life essence of enslaved magical creatures. It takes place in a (then) present-day in which, for example, your taxi is a flying carpet, but otherwise the same (cabbie, meter, and so on). With all that said, a sci-fi setting with no supernatural/fantasy elements could readily substitute actual magic with alien phlebotinum in the equation.
In these circumstances the machine would work without the magic, but magic improves it.
There is "technomancy", the school of magic that specializes in controlling or improving existing technology with magic. Fantastic Science leads to this because it treats magic as science something to be studied and learned and experimented with. In some works, technology is based on sufficiently advanced magic, which is itself disguised sufficiently advanced technology. When Magitek is combined with gritty realism, we get Dungeon Punk, but magitek is also common in comedic fantasy.