The brooch almost certainly belonged to the wife, or love, of the last prince of Cardolan.
This is suggested by the "some say" in Appendix A to The Lord of the Rings.
‘It is said that the mounds of Tyrn Gorthad, as the Barrowdowns were called of old, are very ancient, and that many were built in the days of the old world of the First Age by the forefathers of the Edain, before they crossed the Blue Mountains into Beleriand, of which Lindon is all that now remains. Those hills were therefore revered by the Dúnedain after their return; and there many of their lords and kings were buried. [Some say that the mound in which the Ring-bearer was imprisoned had been the grave of the last prince of Cardolan, who fell in the war of 1409.]’
Aside from this statement, we know that the barrow Frodo was in was used by the Dunedain, not the Men of the First Age. It contained weapons forged explicitly for the war against the Witch-King of Angmar. Tom Bombadil tells us as much in the Fog on the Barrow-downs chapter..
For each of the hobbits he chose a dagger, long, leaf-shaped, and keen, of marvellous workmanship, damasked with serpent-forms in red and gold. They gleamed as he drew them from their black sheaths, wrought of some strange metal, light and strong, and set with many fiery stones. Whether by some virtue in these sheaths or because of the spell that lay on the mound, the blades seemed untouched by time, unrusted, sharp, glittering in the sun.
‘Old knives are long enough as swords for hobbit-people,’ he said. ‘Sharp blades are good to have, if Shire-folk go walking, east, south, or far away into dark and danger.’ Then he told them that these blades were forged many long years ago by Men of Westernesse: they were foes of the Dark Lord, but they were overcome by the evil king of Carn Dûm in the land of Angmar.
‘Few now remember them,’ Tom murmured, ‘yet still some go wandering, sons of forgotten kings walking in loneliness, guarding from evil things folk that are heedless.’
The latter paragraph tells that Tom is thinking of the Men of Arnor: he specifically refers to Aragorn and his line.
The narrator confirms in The Battle of Pelennor Fields that it was forged by the men of Arnor, specifically for use against the Witch-King of Angmar.
So passed the sword of the Barrow-downs, work of Westemesse. But glad would he have been to know its fate who wrought it slowly long ago in the North-kingdom when the Dúnedain were young,- and chief among their foes was the dread realm of Angmar and its sorcerer king. No other blade, not though mightier hands had wielded it, would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.
So, we know for a fact that the contents of the barrow must have been placed there between 1300, when:
c. 1300 Evil things begin to multiply again. Orcs increase in the Misty Mountains and attack the Dwarves. The Nazgûl reappear. The chief of these comes north to Angmar. The Periannath migrate westward; many settle at Bree. 1356 King Argeleb I slain in battle with Rhudaur.
and shortly after 1409, when:
It was at this time that an end came of the Dúnedain of Cardolan, and evil spirits out of Angmar and Rhudaur entered into the deserted mounds and dwelt there.
after which the Dunedain would have ceased to use the Barrows.
Further, we know that the Barrows fell within the bounds of Cardolan, not the other three kingdoms, we we would expect the Cardolans to be over-represented, especially by the time of the war with the Witch-King (when the blades were forged), since the three kingdoms were at war with each other prior to the war with Angmar.
After Eärendur, owing to dissensions among his sons their realm was divided into three: Arthedain, Rhudaur, and Cardolan. Arthedain was in the North-west and included the land between Brandywine and Lune, and also the land north of the Great Road as far as the Weather Hills. Rhudaur was in the North-east and lay between the Ettenmoors, the Weather Hills, and the Misty Mountains, but included also the Angle between the Hoarwell and the Loudwater. Cardolan was in the South, its bounds being the Brandywine, the Greyflood, and the Great Road.
In Arthedain the line of Isildur was maintained and endured, but the line soon perished in Cardolan and Rhudaur. There was often strife between the kingdoms, which hastened the waning of the Dúnedain. The chief matter of debate was the possession of the Weather Hills and the land westward towards Bree. Both Rhudaur and Cardolan desired to possess Amon Sûl (Weathertop), which stood on the borders of their realms; for the Tower of Amon Sûl held the chief Palantír of the North, and the other two were both in the keeping of Arthedain.
But more than that, we have to consider Bombadil's account that "fair was she" who wore it and "we will not forget her." The clear implication of Bombadil's statement was that he personally knew or saw the woman who wore the brooch. And what do we know about what the people of Cardolan were doing in the war in 1409?
A great host came out of Angmar in 1409, and crossing the river entered Cardolan and surrounded Weathertop. The Dúnedain were defeated and Arveleg was slain. The Tower of Amon Sûl was burned and razed; but the palantír was saved and carried back in retreat to Fornost, Rhudaur was occupied by evil Men subject to Angmar,21 and the Dúnedain that remained there were slain or fled west. Cardolan was ravaged. Araphor son of Arveleg was not yet full-grown, but he was valiant, and with aid from Cír-dan he repelled the enemy from Fornost and the North Downs. A remnant of the faithful among the Dúnedain of Cardolan also held out in Tyrn Gorthad (the Barrow-downs), or took refuge in the Forest behind.
So we can almost certainly say the barrow was the burial place of people of Cardolan, and that there's no reason to dispute the textual suggestion that it was the grave of the last prince of Cardolan and possibly also his wife, or lover - if she had not died prior and the brooch buried with him, as a memento he had kept with him after her death.