Ultima Underworld II he are two rooms with Steel doors that are at the south end of the level 3. one you cross a bridge the other you have to swim or walk across the water for.

Where do I fine the keys to open these doors?

Thank you

those doors dont have keys to my recollection
te left one can be bypassed from a passage at water level
just past the bridge that lead to the massive door

the other one you have to pick or use some means of magicaly opening it

of course i may be wrong about there not being a key for these doors

I think Charles in the castle gives you a key for one of them at one point in the plot.

Apart from that, Vyraexii is right, the Open spell is the easiest way. You can prepare it in another world, then run back through the gem and all the way to the door in the castle sewers to use it.

That is correct.

In this room is also a chest with a moonstone. Once you have found the other moonstone, you should be able to gate travel into that room. The chest also contains a key to the door, to prevent you from being trapped.