A scene in Dragon Age: Inquisition (that can be seen here) shows that Empress Celene and Briala (her elven handmaid and spymaster) were once in a secret romantic relationship. As the scene progresses, the player helps bring them back together, though the romantic aspect of their relationship still seems to be a secret. This is only one of several possible outcomes however, and can only be achieved if particular conditions (outlined here) are met.
Apparently, Celene would be willing to marry a man for political purposes (see here and here), but the game is written in a way that seems to suggest she identifies as a lesbian. A book written by Patrick Weekes, called Dragon Age: The Masked Empire, explores her relationship with Briala in more depth.
LGBTQ references in this game series:
Dragon Age II (2011): Serendipity
Heroes of Dragon Age (2013): Maevaris Tilani
Briala. (n.d.). Retrieved from http://dragonage.wikia.com/wiki/Briala
Celene Valmont I. (n.d.). Retrieved from http://dragonage.wikia.com/wiki/Celene_Valmont_I
FluffyNinjaLlama. (2014, December 27). Dragon Age: INquisition- Celen & Briala still in love. YouTube. https://www.youtube.com/watch?v=gEkKlgJX8Bc
Romancing empress Celine. (n.d.). Retrieved from http://dragonage.wikia.com/wiki/Forum:Romanceing_empress_Celine
Tor.com. (2013, March 29). Tor Books Announces New ragon Age novel with BioWare Senior Writer Patrick Weekes. Tor.com. http://www.tor.com/2013/03/29/tor-books-announces-new-dragon-age-novel-with-bioware-senior-writer-patrick-weeks/
Wicked Eyes and Wicked Hearts. (n.d.). Retrieved from http://dragonage.wikia.com/wiki/Wicked_Eyes_and_Wicked_Hearts
Will Empress Celene appear in DAI? (2014, July 29). Retrieved from http://forum.bioware.com/topic/510420-will-empress-celene-appear-in-dai/