A microwave can be a great alternative, but there are potential hazards to be aware of. Considerations of "safe" relate to both your material and the microwave and containers you're doing the drying in.
This question and answer was triggered by something I've done successfully dozens of times, and today resulted in my material being contained in a molten blob of plastic fused onto the microwave turntable. The specifics of my disaster might be a bit unusual, but I'll include information that will apply to many situations where people might want to use the microwave to dry stuff.
Low power settings
On a regular microwave, low power settings are actually full power for a fraction of every minute. An inverter microwave reduces the power level. On my inverter microwave, the inverter only goes down to 40% power, so a level like 10% is actually 40% for the first quarter of each minute. You need to know how your own microwave implements power settings.
Microwaves don't heat material evenly throughout; they get absorbed by the material as they pass through and most of the heating is near the surface. The hot material then spreads the heat into the surrounding material and the temperature equalizes. At low power settings with a normal amount of material, the material doesn't get too hot during the power cycle and then cools a bit during the off part of the cycle as the heat spreads around. Some of the heat from the warmed material also dissipates into the oven environment, warming other things.
If you're working with small amounts of material, the burst of full power (or 40% power in my case), can make the material hot if that's the only thing absorbing the energy.
How things heat during normal microwave operation doesn't scale to what happens with small amounts of material. It isn't small differences in behavior, it can be huge differences, and things, both good and bad, can happen much faster than you expect.
Hot spots
The inside of the microwave gets nodes of high energy (hot spots), and low energy. There are interesting YouTube videos of people heating a large thin pancake, and the node pattern makes art on the surface.
Those hot spots also work vertically. On my microwave, there's a lot more heating at turntable level than several inches above it (as I now have learned).
If you have a lot of material distributed around the turntable, the heating can equalize. But if you have a small amount, and it is in one spot, it's different. The material can heat much faster, or if it mostly passes through areas of low energy, a lot of the energy ends up getting absorbed by other things, heating things other than your material.
What gets heated
When you work with small amounts of material and long run times, even at low power, many things don't behave as you're used to. A few are mentioned above. Here are more. Under the category of Things that normally don't get hot, get hot :
The water that evaporates from the material goes into the air inside the microwave. It's still water. The more you dry the material, the more of its water is floating around inside the oven, getting in the hot spots because it can go everywhere, and turning to steam. The steam heats other things in the microwave, like your container and the turntable glass.
As your material dries, several things happen. The remaining water in your material heats faster and makes the material hotter. And more and more of the energy and heat is being transferred and absorbed by things other than your material, so they get hot.
Many materials aren't much affected by microwaves when they're at room temperature. But if they are hot, they absorb microwaves and get hotter. The hotter they are, the hotter they get. Glass is one of those. There are YouTube videos of people preheating a glass bottle, and then melting it in the microwave (no kiln), and turntable glass that started out hot, and then the microwave got it glowing red hot. When you run the microwave for a long time, even at low power, and there isn't much material in it, and it is also being heated by the steam from your material, the glass will start to get very hot.
Many microwave-safe materials are safe for their intended use, based on some assumptions about how they will be used. For example, some microwave soup comes in a heavy-duty polypropylene cup. You peel off a seal at the top and stick it in the microwave. Ninety seconds later, you have hot soup. When you're done enjoying the soup, wash out the container and you have a free, heavy-duty, microwave-safe cup for you projects.
Polypropylene is virtually unaffected by microwaves, but some of the materials added to it for coloring and other properties, can be slightly affected. But it's in minute amounts, and the container is full of soup, so the effect is irrelevant. Guess what happens if you use it to hold a small amount of material, the material stays in a low-energy area, and you let it run for half an hour? Your material doesn't get all that hot, but the container absorbs a lot of energy.
Guess what happens if it is also sitting on a glass turntable that is getting really hot? It quickly goes from semi-hot liquid in a soup cup to a melted plastic container, "hot-glued" to the turntable.
What things to avoid drying in a microwave
A general conclusion from my disaster is that small amounts of material are a problem. Small amounts and microwave ovens aren't a good combination, and things that otherwise wouldn't be a problem can become a problem. If you need to use a microwave for small amounts, don't use power cycle timing. If you have an inverter microwave, set it on the lowest power that actually uses that power 100% of the time. Manually control the time for each microwave exposure.
In addition to the considerations above, there are some materials that generally would be better not to dry or dehydrate in a microwave. This is by no means intended to be a comprehensive list, just a few things off the top of my head:
Cellulose-based materials. If you have something like soaking wet paper and you want to dry it to damp, and you will be carefully monitoring it, that will probably be fine (as long as the heat, hot water, and steam won't affect whatever it is). However, paper and other cellulose materials can be super-dried in a microwave, and get very hot. It can be damaged (become brown and brittle), and even ignite under certain conditions.
For that reason, I also wouldn't use it to dry plant specimens, like for a herbarium.
Dehydrating mineral materials. Certain common materials change form when they absorb water, and you can sometimes reverse the process by removing the water. For example, calcium chloride, which is used as a desiccant. You start with pellets of calcium chloride. As it absorbes moisture from the air, it goes into solution. Rather than discard the solution, you can dry it out, turn it back into solid form, and reuse it.
It isn't an issue to do that kind of thing in an oven. But you need to be careful doing it in a microwave. When materials go from liquid to solid, there may be heat of crystallization--a lot of additional energy that needs to be either added or removed for it to change state. It can do unexpected things with time and temperature in a microwave, and potentially damage the container.
