I thought I'd read that rules for Oath would be included in the Horse-Lords supplement. Maybe they will be in the adventure supplement Oaths of the Riddermark (as the Holding rules can be found in the Darkening campaign).
But ever since, I've also given a thought on how this rules could work. There's a quote by Gimli and Elrond that, I think, summarizes exactly how Oaths should be represented in game. I haven't come up with any wonderful mechanic for it, but there are some aspects I think should be included:
'The others go with him as free companions, to help him on his way. You may tarry, or come back, or turn aside into other paths, as chance allows. The further you go, the less easy will it be to withdraw; yet no oath or bond is laid on you to go further than you will. For you do not yet know the strength of your hearts, and you cannot foresee what each may meet upon the road.’
‘Faithless is he that says farewell when the road darkens,’ said Gimli.
‘Maybe,’ said Elrond, ‘but let him not vow to walk in the dark, who has not seen the nightfall.’
‘Yet sworn word may strengthen quaking heart,’ said Gimli.
‘Or break it,’ said Elrond.
1) It should play with the Hope and Shadow mechanic. A first point should read something like this:
Gain X extra Hope points that can only be used for acts aimed at fulfilling your Oath.
As with Traits, the player should invoke his Oath and explain how the act (skill test) he is doing relates to it. The LM and the rest of players can decide if it makes sense and the Hope point can be spent. The LM has the last word.
How much should/can this X points be? This could be dependant on different factors: on the greatness of the Oath, for example. As happens with Shadow points -when the LM decides that some situations might grant only 1 point, while others grant 5-, the player and LM could decide how many extra Hope points is the Oath worth. Swearing to a mother to bring back her son from a goblin's den that is located in a nearby mountain coulg grant 1 extra Hope point. But "vowing to pursue with vengeance and hatred to the ends of the World Vala, Demon, Elf or Man as yet unborn, or any creature, great or small, good or evil, that time should bring forth unto the end of days, whoso should hold or take or keep a Silmaril from their possession.", as Fëanor and his sons did, should grant many more points... and carry greater consequences.
Also, powerful individuals seem to be able to swear greater Oaths (Fëanor, Elendil and Elendil's heir). Probably the maximum amount of Hope points that can be gained should be somehow limited by the Valour and/or Wisdom score of the Oathtaker or the "Oathwitness" (as was Isildur). A starting point could be that the maximum number of Hope points that can be gained are the sum of the Valour and Wisdom scores.
The first quote from Gimli and Elrond specifically says that an Oath might "strengthen quaking heart". I've related this to gaining extra Hope points, knowing also that the Hope score is related to the Heart Attribute. But other effects might be also contemplated, taking the quote more literally.
For example, increasing the Basic Heart Score of the Oathtaker by a certain amount only for Attribute bonuses (i.e. when spending Hope points) related to the Oath. Remember that Heart is the Attribute for Fear and Corruption tests. The increase could be equal or be related to the Valour score. The cultures with the lowest Heart score (Dwarves, Elves and Dunledings) could be the ones with more tendency to swear Oaths. Also, those individuals that choose Valour over Wisdom would also favour them (great warriors and war-like cutures, like the eóthéod and, again, dwarves, noldor and dunledings). For a Hobbit, swearing an Oath should be of little benefit, for example. That would explain why Gimli was so eager to swear an Oath to the Fellowship of the Ring, while Elrond, knowing the effect in Shadow increase it would have for the Hobbits, discouraged it. This kind of bonus would stick with the Oathtaker as long the Oath is not fulfilled, while the Hope bonus will dwindle with time, even if the Oath is still "running on". Both options could be ok, in my opinion. Or even a third way could be found, where the extra Hope points are refilled at the end of each year (each Year's End Fellowship phase).
2) But then, there are the bad and dangerous consequences of swearing an Oath, and it should relate to gaining Shadow points.
This vow shall descend to my heirs, all such as may come after me in our new land, and let them keep it in faith unbroken, lest the Shadow fall upon them and they become accursed
I'd say this should happen in two ways:
A) Gaining lots of Shadow points if the Oath is failed or broken. For starters, I'd go with double than the number of Hope points that were gained. The unspent extra Hope points would be lost, of course. In fact, it could even be ruled that the same amount of extra Hope points that were gained should be returned. This could lead to a character losing all his Hope points. Or even that the unspent extra Hope points are lost AND a certain amount of your own Hope points, too.
B) Gaining one automatic Shadow point
for each year (Year's End Fellowship phase) that the Oath is not fulfilled. That is important, as it means that the obsession with the Oath grows stronger (and is more dangerous) each year, until a simple Heal Corruption is not enough to overcome it and the Oathtaker is either forced to fulfill the Oath, or to break it and face the grim consequences. I'm convinced that swearing an Oath should have some kind of exponential danger, so that it impels the Oathtaker into action.
A note on this: Some Oaths, like that of Eorl or the dunledings, could be special in that they swear to act in a certain way if something else happens (go to war if called for aid). In these cases, the consequences of swearing an Oth (both the extra Hope and the yearly Shadow points gained) should only be "activated" once the trigger appears. If the Oath is not answered as it was sworn, it counts as an Oathbreaking with all its consequences, without the gaining of any Hope point.
The years lengthened. The embers in the heart of Thorin grew hot again, as he brooded on the wrongs of his House and the vengeance upon the Dragon that he had inherited. He thought of weapons and armies and alliances, as his great hammer rang in his forge; but the armies were dispersed and the alliances broken and the axes of his people were few; and a great anger without hope burned him as he smote the red iron on the anvil.
In this quote we see how Thorin uses all his Fellowship Undertakings to Heal Corruption with Craft tests in a Sanctuary. And probably he has spent all his extra Hope points gained by the Oath...
Particulary for dwarves, the Stiff Neck of the Dwarves Virtue allows them to grow stronger the older the Oaths become unfulfilled. Dwarves are to be more feared the older their grudge or sworn revenge is!
Other concerns:
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The place where the Oath is sworn.
It seems that every Oath takes place in a special geographical location. I don't know what this should imply in game mechanics, but it is an important part, at least for roleplaying pourpouses. At least we should say that the place is where the Oath is linked to. Earth is a creation of the Song, and maybe is the way to link the Oath with the Creation and, therefore, with the Valar and Eru himself. If the Oath is broken, the Oathbreaker will be tied in some way to that place. The Dead Men of Dunharrow are a good example, but I don't have others.
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Dying trying to fulfill an Oath vs. Breaking an Oath.
The dunledings broke their Oath, and were condemned to turn into restless spirits tied to the place where they swore that Oath.
The sons of Fëanor (as far as I know) didn't break the Oath; they died trying. Therefore, they didn't turn into wraiths tied to the high court of the King upon the summit of Túna.
The rohirrim rode into the Fields of Pelennor thinking that their forces wouldn't be enough to help Gondor destroy Sauron's forces. They had to choose between breaking the Oath and becoming a condemned people, damned to perish as the dunledings did (and maybe be tied to Elendil's tomb), or die trying.
And we know what they chose

:
Ride now, ride now! Ride to Gondor!
'Here is the mid-point of the Kingdom of the South, and here shall the memorial of Elendil the Faithful abide in the keeping of the Valar, while the Kingdom endures. This hill shall be a hallow, and let no man disturb its peace and silence, unless he be an heir of Elendil.” I have brought you here, so that the oaths here taken may seem of deepest solemnity to ourselves and to our heirs upon either side.'
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Individual vs. Group vs. Cultural Oath
Maybe there could be a difference between:
1) swearing an Oath yourself ("I swear upon my sword to bring your song back from the clutches of the goblins!")
2) swearing in group for a certain goal ("We'll go to Mordor with you!"). This could mean that the extra Hope points are added to the Fellowship pool, instead of to each individual, and it's the groups goal what has to be invoked. Each hero/brother/member of the group that leaves it won't benefit from the Fellowship pool anymore.
3)or the Oath of a whole culture, made by its king ("This vow shall descend to my heirs, all such as may come after me in our new land, and let them keep it in faith unbroken"), which would mean that every hero belonging to that culture would be tied to that Oath.
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Oaths unfulfilled by the fathers descend to their heirs.
If a newly created hero wants to benefit from the Heroic Heritage (Revised Book p.282) bonuses of a retired hero that had an unfilfilled Oath, then he has to inherit the Oath also (as if taken anew).
The embers in the heart of Thorin grew hot again, as he brooded on the wrongs of his House and the vengeance upon the Dragon that he had inherited.