You can immerse the egg in a mug of water so that heat is transferred in more slowly; I've done it when no stove was available.
It's not necessarily a time-saver, though.
BTW, whole potatoes can also explode unless pierced many times, I have found to my regret.
It produces instant mashed potatoes -- all over the oven.
lifehacks.stackexchange.com/users/2012/DrMoishe Pippik
I found simply covering the eggs completely in a mug and adding a tablespoon of salt to the water prevented any explosions.
Ran the microwave on full for ten minutes, took it out and sat it for two minutes.
Transferred to a bowl of cold water for another two minutes and then shelled it.
Perfect hard-boiled egg with no grey ring.
:)
lifehacks.stackexchange.com/users/10479/KayDee
You can use a toothpick to place a small hole in the ends of the egg puncturing the membrane.
This allows pressure to escape.
It will also allow some egg to escape as it expands, but not too much.
Place it in water as mentioned above.
I haven't done this in a few years, but I think 1.5 to 2 minutes is the cook time.
lifehacks.stackexchange.com/users/11118/Quackage
I've been using the Nordic Ware Microwave Egg Boiler for a few years.
Depending on the size of the eggs, you'll need between 6.5 and 8 minutes at 1100 watts.
Once you've settled on a brand and size of eggs, you can get them perfect every time - hard boiled, soft yolk etc.
by tweaking the cooking time between those two values.
Fantastic gadget, 4.5+ stars on Amazon with over 1200 reviews.
lifehacks.stackexchange.com/users/2201/Dan Dascalescu
Using an Inverter Microwave , I bring a bowl of water to a boil first thenput in the egg(s) and then use 20% power to keep the water at a simmer.
Timing depends on how many eggs and whether you want soft or hard boiled eggs.
If I'm hard boiling a dozen or more eggs
I use a pressure cooker.
lifehacks.stackexchange.com/users/12793/Thoraldus
Frameshift:
You want to boil an egg easily, so your first instinct is the microwave.
Instead may I recommend an even easier way, the rice cooker!
Put a cup of water in the bottom of the cooker and place as many eggs as you want in the plastic basket that comes with it.
Then press "steam" for 15 minutes.
Your eggs are done!
I've recently discovered rice cooker cooking
and it's made everything so much easier.
The rice cooker maintains boiling water at the perfect temperature so you don't have to stand over the stove watching it to make sure the water doesn't boil over.
Instead, you press a couple buttons and then relax.
I use the steamer basket to cook all sorts of things like frozen fish (no dethawing needed) to frozen veggies, not to mention putting rice and grains in the bottom part and you have an complete meal just like that.
I think anyone who's impressed by the convenience of the microwave, should add a rice cooker to their kitchen.
lifehacks.stackexchange.com/users/27593/SurpriseDog
Here are few ideas: use a microwave safe bowl or cup with just enough water to cover the eggs and boil the water without eggs , then turn the heat off and put the eggs in for 12-15 minutes (soft or hard) using medium power, Consider adding 1/4 teaspoon of vinegar and salt, and cover the dish.
wrap each egg in a piece of aluminium foil (make sure that whole shell is covered) and put it into water - foil prevents the microwaves from penetrating the shell causing exploding eggs and water in the foil should prevent the arcing.
Warning :
Be careful, as too high temperature for too long can even blow open the door of your microwave, so proceed with caution .
Source: Boil an egg in the microwave at Cooking SE
Further read:
Microwave ovens should warn of exploding eggs at New Scientist
What's the right way to hard boil eggs? at Cooking SE Microwaving scrambled eggs at Cooking SE Towards the perfect soft boiled egg by Martin Lersch How to Cook an Egg in the Microwave at Better Homes
lifehacks.stackexchange.com/users/2272/kenorb
It's quite dangerous to hard-boil an egg in the microwave as it may simply explode and making a big mess. Cleaning the microwave after that kind of accident to avoid a bad smell can be a miracle.

Are there any safe methods of hard-boiling an egg in the microwave?
How to hard-boil an egg in the microwave safely?
lifehacks.stackexchange.com
<food><kitchen><temperature><food-safety>
lifehacks.stackexchange.com/questions/4007
lifehacks.stackexchange.com/users/2272/kenorb
There are a few different techniques for hard-boiling an egg in the microwave safely. One simply way is to immerse the egg in a mug of water for ten minutes and then transsfer it to a bowl of cold water for two minutes. You could also use a toothpick to place a small hole in the ends of the egg, thus allowing the air to escape as it cooks. You might want to also consider a Nordic Ware Microwave Egg Boiler. The options are to put the egg in a mug of water and then put the mug in the microwave, to make small holes in each end of the egg with a toothpick and then place in water in the microwave, to use a special microwave egg boiler or to use a rice cooker.
Put the egg in a mug full of water and then put the mug in the microwave. Make a small hole in the ends of the egg with a toothpick and then place in water in the microwave. Use a microwave egg boiling device like the Nordic. Bring a bowl of water to the boil in an inverter microwave and then add eggs and simmer. Put the eggs in a rice cooker for 15 minutes.