Groa's son Svipdag is mentioned by this name in two Old Norse songs, Grogalder and Fjölsvinnsmal, which as Bugge has shown, are mutually connected, and describe episodes from the same chain of events.
The contents of Grogalder are as follows:
Groa is dead when the event described in the song takes place. Svipdag is still quite young. Before her death she has told him that he is to go to her grave and call her if he needs her help. The grave is a grave-chamber made of large flat stones raised over a stone floor, and forming when seen from the outside a mound which is furnished with a door (str. 1, 15).
Svipdag's father has married a second time. The stepmother commands her stepson to go abroad and find Menglödum, "those fond of ornaments." From Fjölsvinnsmal we learn that one of those called by this name is a young maid who becomes Svipdag's wife. Her real name is not given: she is continually designated as Menglöd, Menglad, one of "those fond of ornaments," whom Svipdag has been commanded to find.
This task seems to Svipdag to exceed his powers. It must have been one of great adventures and great dangers, for he now considers it the proper time to ask his deceased mother for help. He has become suspicious of his stepmother's intentions; he considers her lævis (cunning), and her proposition is "a cruel play which she has put before him" (str. 3).
He goes to Groa's grave-chamber, probably in the night (verda auflgari allir a nottum dauthir—Helge Hund., ii. 51), bids her wake, and reminds her of her promise. That of Groa which had become dust (er til moldar er komin), and that of her which had left this world of man and gone to the lower world (er ór ljódheimum lidin), become again united under the influence of maternal love and of the son's prayer, and Svipdag hears out of the grave-chamber his mother's voice asking him why he has come. He speaks of the errand on which he has been sent by his stepmother (str. 3, 4).
The voice from the grave declares that long journeys lie before Svipdag if he is to reach the goal indicated. It does not, however, advise him to disobey the command of his stepmother, but assures him that if he will but patiently look for a good outcome of the matter, then the norn will guide the events into their right course (str. 4).
The son then requests his mother to sing protecting incantations over him. She is celebrated in mythology as one mighty in incantations of the good kind. It was Groa that sang healing incantations over Thor when with a wounded forehead he returned from the conflict with the giant Hrungner (Gylfag.).