The easiest way possible without having to farm Nisha for the Sheriff's badge: At the final quest in the game (Talon of God) you have the option to visit every NPC to help you (Marcus, Scooter, Moxxi, Hammerlock, Tannis, Dr Zed) before traveling to Eridium Blight.
Everybody will give you something of a weapon, except for Tannis, who gives you a relic. After she is done doing her speech, she gets a relic at total random. Most relics are either blue, while there are purple relics in the loot pool. When she gives you a blue relic, quit, reload your save. She will do her dialogue again and offer you a relic. Save and reload until she gives you a purple relic. (Mine was a 20.9% quicker shield refill)
If you can wait and have the patience and time: You can also wait for your Ultimate Vault Hunter Mode playthrough. Legendary Loot Midgets seem to carry E-tech relics since relics are more important in this mode.