Click here for more info on the East Empire Blessings and how convincing the Jarls works.
The following options are available for Elisif.
The "Crown of High King Torygg" will unlock the gift option for Elisif.
The first clue that starts this quest is a note that can be found on a nightstand in Elisif's bedroom named "Note to Elisif the Fair". Reading this will give the player an objective to visit the Silver-Blood Inn in Markarth.

In the room with two beds (when entering, walk to the back of the inn and turn right), the player will find a (somewhat hidden) note prompting them to visit the Cidhna Mines by getting themselves arrested, and finding a man named Rot-gut.

Inside Cidhna Mines, the player will find Rot-gut (from the entrance, turn right and go down). He will become hostile when the player interacts with him. Once killed, he can be looted for the "Key to Crown Strongbox". The objective will next point the player to a safe in Liar's Retreat.

The safe can be found in the back of Liar's Retreat behind a Novice-locked door. Inside, the player will find the Crown. Looting this will prompt them to return to Elisif.
