Ashley and Wynonna Judd were on hand Sunday at the CMA Theater in Nashville, where the Judds were inducted into the Hall. Of course, Naomi -- who made up half the duo -- had suddenly passed the day prior ... so her kids stepped up.

Their speeches were sorrowful and moving -- both AJ and WJ were weeping ... explaining how much Naomi knew she was beloved by all, which is what they say kept her hanging on for as long as she did.

Ashley also asked folks to come and see their widowed father, Larry Strickland. When Wynonna spoke, she offered up some much-needed humor ... but then said what everyone else was thinking -- that she was broken and at a loss for words.

Wynonna accepted her medallion -- and everyone gave her a huge round of applause. It was incredibly emotional all the way around ... and sorta astonishing that the Judd sisters even made it considering the shock of their mother dying.

As we reported ... Ashley and Wynonna announced Naomi's death Saturday, citing mental illness, but nothing more. Naomi was out publicly alongside Wynonna in recent weeks ... and was fully expected to make the ceremony, with no outward ailments anyone was aware of.

Naomi had been open about her mental health struggles over the years, saying she'd battled depression for a long time. The exact circumstances surrounding her death remain unclear.