Skyrim Walkthrough: Ep. 73 Finding Ebony Ingots

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The best location I found is Gloombound Mine which is part of an orc camp south-east of Windhelm.

I found 42 ebony ore and some iron ore as well as some diamonds and other gemstones. You aren't welcome in the mine, but the orcs won't do anything to get you out of the mine.

Sometimes I find that an ore vein is occupied. I usually like to kill the occupant so I don't have to wait for them to move, which they will do eventually. Be sure to be on the look out for any air distortions because that could mean that there is flamable gas around. It usually looks like:

It is hard to tell on the image, but if you look at the video below it will be quite obvious. If you do ignite the gas it does a little damage, but it didn't kill me. I did have very good armor and was a high level so if you are a lower level you have to be more careful with it.

After you have collected the ore you need to find a smelter to turn the ore into ingots. Usually there is a smelter near mines, just look around for a bit