[Burningkrome]

I see a number of "microwave safe" aluminum and steel products on the market. Searching the general internet leads to a lot of inconclusive and unauthoritative answers. I've seen discussions on "smooth edges", coatings, etc.

Can anyone describe (or link me to a reliable reference describing) the science behind when, why, and how metals can be safely used in a microwave? 

[Enthalpy]

You mean, a kitchen microwave oven? Radars would be a different topic.

All metals are basically a short-circuit to microwaves, whatever the base metal and alloy. Expect them to shield the contents from heating, excepted for locations where a fading wave has some significant intensity, say the upper middle of a cup.

If the field has a significant vertical component and the non-magnetic metal part is flat, this component will remain and heat the contents. Certainly not what the manufacturer of the oven desires. The field direction isn't uniform within an oven neither. Protections in the oven may or not detect an anomaly and stop operation.

Alloying and partial sintering can increase a metal's resistivity, but it's still a short-circuit as compared with air. A load of metal powder in a polymer would insulate, but do you accept this as a "metal"? Or small metal parts embedded in a ceramic?

What can be done for small parts is avoid at least the sparks and corona in the air at the edges of the metal part. The metal's short-circuit leaves more voltage available to produce a strong gradient in the air, and sharp edges concentrate the field there. Round edges (in both dimensions) alleviate this. If you're lucky and the metal part is small enough, it won't make zap. The best effect I see from coatings is to produce no poisons when sparks occur.

[Burningkrome]

@Enthalpy

Thanks for the detailed reply. I should have offered more detail in the original post. I am speaking of the traditional kitchen microwave ovens for food. I'm also thinking specifically of the safety (AKA damaging the oven) of placing steel which is surrounded by ceramic fiber.

In detail, actual case is using a "microwave kiln"* (a solid ceramic fiber shell, lined internally with silicon carbide.) The steel object (an 80mm x 50mm x 2mm hollow cuvette tube - basically a bit of steel pipe with a 2mm thick wall) is placed inside the ceramic microwave kiln. The goal is actually to have all the microwaves absorbed by the silicon carbide. I.e. nothing inside the steel tube itself needs to be heated directly by the microwaves, but is instead warmed by the heated carbide.

I understand that these "microwave kilns" have been used for glass beads, and small gold/silver/bronze metal clay projects. But there was some concern expressed that steel - especially such a large bit of steel - might cause damage to the oven (by sparking) even if it's surrounded by the ceramic "microwave kiln." Note that the steel pipe is not tightly wrapped by the ceramic, but sits within the open space inside the kiln. The steel tube is well polished on all edges.

My initial instinct would be that this should work fine. But, again being such a large bit of steel, I thought I'd ask before experimenting with blowing my oven up.

*https://depts.washington.edu/open3dp/2010/04/microwave-kilns/

[Enthalpy]

I feel impossible to make a numerical opinion about that situation. My best answer is only: try and observe. Sparks may damage the fibres but probably not the oven.

I expect the microwaves to reach the metal with nearly full intensity. The SiC foam should absorbs them slightly: enough to get hot and catch an interesting portion of the available microwave power, but no significant shielding. Unless the foam part conducts better than some 400Ω.

The composition of the metal won't change usefully the risk of sparking. Only the shape does. Very round edges at the tube's ends would improve. Closed ends are better than an open tube. Ceramic coating there can improve too by reducing the field through permittivity and by withstanding higher fields. This needs a significant thickness (until the field has spread into more area), and a good design isn't trivial, but less efficient tinkering is conceivable.

The composition of the metal does change the ability to withstand heat. Aluminium is just bad, usual and special stainless steel far better, then you have nickel alloys for gas turbines, and beyond that only exotic materials. Corrosion, creep, and sublimation limit the capability, where materials beyond nickel superalloys can withstand corrosion and sublimation but creep badly.

Magnetic permeability lets absorb microwaves over an even shallower depth ("skin effect"). I expect no consequence here: in all cases, heat diffusion is what will limit the skin temperature.

The gas composition can help. Already drying the air limits sparking. High pressure increases the breakdown field almost linearly. Some gases are better: SF₆ best, CF₄ excellent, dry air good. Deep vacuum would be excellent too.