In the Kaddish, we say that may G-d be praised "beyond any blessing, hymn, praise, and consolation said in this world."
I understand how we can bless or praise G-d -- but how exactly (or even fuzzily?) do we console G-d?
Based on Dave's comment, so hat tip to him:
The Rokeach here says that the nechama (consolation) we provide is on G-d's regret for destroying the Temple, as He missed out on the nice singing that would occur if the Temple remained extant. As such, he recommends that the prayer leader lengthen the word V'nechemata", and think of consoling G-d and consoling us (presumably those praying or the Jewish people in general).
I have heard in the name of Rav Hirsch (though I lack a specific citation) that nechama can be a change of mind, not only consolation. This Rokeach seems to fit that meaning, in that G-d changes His mind from destroying the Temple to, if it is possible to say, wishing that He had not done so, similar to: וַיִּנָּ֣חֶם יְהוָ֔ה כִּֽי־עָשָׂ֥ה אֶת־הָֽאָדָ֖ם (and G-d regretted having made man).
No source, just my thoughts, but here goes. The Kaddish has a strong association with mourning. One way we comfort mourners, especially through Kaddish, is by reminding them that HaShem has a plan and that their suffering isn't for naught. This can be a great source of comfort to a mourner, and that itself is a great praise of HaShem. As such, the praise of HaShem's consolation is a fitting threshold for comparison for just how much HaShem should be praised (especially in the Kaddish itself).