Question: I am early in this design but am imagining a fictional world in the age of exploration including classic fantasy tropes of monsters and magic, with renaissance era technology, that is cannons, muskets, clockwork and wacky renaissance war machines perhaps entwined with magic albeit to limited effect or making use of fantastical beasts. I would like the world to stay in this state of technology for as long as possible.

So I indeed ask, What would stop advancements in technology beyond this state? Specifically weaponry?

Answer: 
Interchangeable parts don't.
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No, *seriously* - I don't just mean there are poor tolerances in your manufacturing. I mean that having all those blasted wizards running around tapping into arcane essences of space, time, thought, logic, and reality ... it means that an inch in Chicago isn't always more than seven-eighths in New York. It means a cartridge loaded in your basement might not be reliable in the woods behind your house.

The most practical technology for your scenario is *crude* tech with very *high* tolerances, so that you can't be disappointed. Load up a blunderbuss with thimbles, forks, and hope (and a mass of black powder casually poured from a horn) ... and it has no more uncertainties than it would in our world.
Magic has to be superior to technology.
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The development of weaponry didn't happen in a vacuum, it was in response to battlefield conditions. People stuck with firearms and continued to improve them because they were effective against the defenses they encountered. So if you don't want certain types of weapons to advance, make them ineffective. The obvious solution is to have magic render bullets as harmless with trivial protective wardings, or something along those lines. Something where the magical protection is far easier than the mundane weapon it defeats.

This creates a new problem: why are people using ineffective weapons at all? At what point did magical protections become common in warfare? That's the point where you'd see mundane weapon development stall out. So think about when this happens, and why. What changed to make magical protection commonplace? And how do armies defeat it? Probably with magical weapons of some kind.

So your task is to think about how this society uses magic to wage war, and to devise reasons for why building more advanced machines never seemed like a feasible or worthwhile idea to get the edge over the enemy. I think for this to be the case **magical solutions have to be cheaper, easier to use, and more readily available than the means to mass produce machines**, as well as more effective.

This should be your guiding principle when thinking about how magic is used if you want it to essentially replace the development of modern technology. It should be accessible to people at all levels of society and be fundamentally superior to the technology it replaces. If technology is easier for a majority of people to access and can defeat magic, nobody would use magic, especially in war.