Woodin gave a consistency proof of a normal $\omega_1$-dense ideal on $\omega_1$ from an almost-huge cardinal. He never published this argument, but it is written up by Foreman in the Handbook of Set Theory. In this article, and in a paper from the 90s, Foreman claims that this argument is adaptable to other cardinals to yield the consistency of an $\kappa$-dense ideal on $\kappa$ where $\kappa$ is the successor of a regular cardinal. I have had great trouble trying to prove this claim, as one crucial part of the argument seems specific to $\omega_1$ (which I will explain if you ask). So does anyone know how to prove Foreman's claim?
This is answered in chapter 2 of my thesis. As far as I know, this is essentially the only method for obtaining such ideals. I am very interested in finding alternative constructions. Please contact me if you have some ideas.