Huh. I just finished reading those books a couple of weeks ago. I won't lie, I've been doing some fair musing on how to replicate the mechanics in Fate Core, but since you didn't give a specific system I'll just air my thoughts anyway, see where they lead me.

In general terms I'd have characters with daemonism be able to craft items within their "strength" of the skill. Skill in daemonism gives them a maximum amount of strength that they can reliably and safely craft, and it'd involve distinct, quantifiable but still freeform effects, which could include things like bonuses at skills (cutlass), automatically succeeding at specific tasks that are not actively opposed (skeleton key), make the characters able to use their daemonism skill in place of other things (tooth, and again the cutlass if you wish to go that route), or just simple minor effects that wouldn't otherwise be possible (communicators, the see-through-walls -effect of one of the Century Knights, etc). Each effect could have its cost and effectiveness scaled to make more or less powerful items. Exact parameters are of course fairly out there.

At the same time, the actual use of these items for their purposes in play would come at a cost. A daemonist would be able to create an item with power beyond their strength limit granted by their skill but increase the drainage it causes (with perhaps a minimum amount, depending on what the item does). If the system separates mental and physical "health", this would cause mental damage. If hit points are abstract, make them cause hit points. Or something else entirely, depending on how the game emulates, but the idea of cost should always be there.

Characters should generally have some sort of limit of daemonic tools they have at their disposal at any given time. How to emulate Bess (the golem, for those who haven't read the books) would likely be done with other rules, an advantage chosen at character creation or other feature, leaving the actual item rules for simpler and personal trinkets.

As for the equipment used in daemonism but not daemonically thralled, it'd likely belong to a separate but related skill, which would essentially mean that a proper daemonist would have two skill dedicated to safely practicing it. They can be powerful but uncontrollable, controlled but weaker, or a balance between the two. It gives a bit of choice in character creation and allows for at least some variety in different kinds of daemonists and how they do things.

This leaves the ritual kind of daemonism, in the sense of summoning and controlling daemons for information, tracking or other one-off uses. This too would be used by the daemonism skill in conjunction with the "control" skill (whatever its name turns out to be). These could be made into single rolls, or into full fledged encounters with multiple rolls depending on the complexity. I'll admit I haven't given this part nearly as much thought.