Hmm. That's a tricky question. My suspicion is that Quenya would use a particular infinitive in this case, though that's a guess. Something like:

ecénielye colitanta i collor héruron

You (pl.) have seen their bearing the cloaks of the lords.

For a similar phrase see:

eldamo.org - Eldamo : Quenya : la navin caritalyas mára

Why not the Present Active Participle? Ecénielyë te cólala i collor héruron (Independant pronoun to differentiate between 3rd pers. Sg., as PPA doesn't form a plural)

I see two possibilities: either use the present active participle as +Severin Zahler says - but I think it would be kolila, per PE22 [1]; or, one can employ the formation from Markirya: ekénielyet akola i héruron kollor

[1] as in English, using the active ppl introduces a slight ambiguity as only the context will tell whether you saw them while you were bearing the cloaks of lords, or they were bearing those cloaks when you saw them

+Severin Zahler We don't have any examples of Tolkien using the active participle as anything other than an adjective, so I don't think it is safe to assume to can be used in all the same contexts as in English. That's why I prefer the particular infinitive. On PE22/154-5 the active participle suffix -ila was described only as "adjectival".

+Tamas Ferencz I agree that the Markiya construct is another possibility, but we don't know how pronouns are used with that syntax.

Based on a process of elimination, I now think that I will use the present participle, since I already know about the -la suffix. I am still a bit confused on how an active participle is used, though. The word "bearing" doesn't seem to be adjectival in the sentence. Otherwise, that is my only concern! Thank you for helping me out!

+Wesley Stump In a book that was very recently published (Parma Eldalamberon #22) the form using -la was described by Tolkien to be adjectival, which is why it may not fit all that well here. Unfortunately the PPA is only very loosely attested :S
I based my solution on the descriptions in Thorsten Renk's "Quetin i lambë eldaiva" Quenya-course, page 88.

The meaning shifts a bit if this "adjectival" is only used like an adjective, it'd mean something like "You have seen the lords-cloak-bearing ones", so it'd loose the focus on the fact that they were bearing these cloaks.

Tolkien's statement in PE22 that the PPA can receive a possessive suffix points to it having a more complex role than just simply adjectival - on the other hand, if you think of it, "bearing" in "have seen you bearing" is kind of adjectival - it qualifies the object.

OK. Thanks for that. I was so confused there! By the way, what is Parma Eldalamberon? I've heard of it, but didn't really know anything about it! Should I read all Eldalamberon from edition 1 or start at 22? Also, what is the Quenya Course you speak of? The only source of Elvish that I use is Council of Elrond .com

+Wesley Stump PE is a journal edited by Christopher Gilson, Carl Hostetter, Patrick H Wynne et al., publishing Tolkien's linguistic essays, drafts & notes. Early issues are probably not that relevant, but I would say for people wanting to study Tolkien's languages in their entirety and in depth, the issues from #12 onwards are an invaluable source. However, many of them are now out of print.
The website is http://www.eldalamberon.com
eldalamberon.com - Eldalamberon Home Page

I'm pretty sure this is a CLASSIC example for an accusativus cum infinitivo (vidisti eos dominorum togas ferre) construction. So I strongly lean towards an infinitive. Ekénielyet cole (cóla) colloi heruon.

A handy page for (possibly) finding an attested solution in these situations is http://eldamo.org/content/phrase-indexes/phrases-q.html — and here is the Markirya poem (containing Tolkien's solution-model to the question at hand at the time of its writing): https://www.jrrvf.com/glaemscrafu/english/markirya.html

Even though I lean towards the active participle, I've noticed that the other half of you think that an infinitive should be placed here. Is there a definite answer, or is this phrase not attested in the language? I find it strange how nobody else had this problem, because I am using quite a popular course. Also, is there a reason why some of you use a k instead of a c?

+Wesley Stump translation often isn't a clear - cut affair, the inner logic of Quenya often differs from that of English, and although we now know much more about its grammar than, say, ten years ago, we don't have a clearly documented rule and example to every situation. Also, Tolkien was famously fiddling with his ideas over the time, so we may have contradicting ideas attested from different periods of his life. Hence the debate.
Now, I am not a native English speaker. Can someone tell me if there is any difference in meaning in these two variants :
You have seen them bear the cloaks of lords.
You have seen them bearing the cloaks of lords.

As for c or k, it's a personal preference. They both represent the same sound. Tolkien mostly used k in his linguistic writings, and c in his published work.

Thank you for that ellaborate answer.

As a native English speaker, I see a very slight difference between those two sentences:

You have seen them bear the cloaks of lords.
You have seen them bearing the cloaks of lords.

Given the use of the present participle in forming the English present continuous (I am walking), the second sentence has a slight implication of continuous action. It's more obvious with a different verb:

You have seen them punch the face of the lord.
You have seen them punching the face of the lord.

The first sentence implies a single punch, whereas the second sentence implies a series of punches.

Since the active participle in Quenya has nothing to do with the present continuous, I doubt there are similar implications in Quenya.

+Paul Strack But since the present continuous can be used as an infinitive (e.g. círa in Markirya), the difference between aorist care ('to make') and continuous cára ('to be making') might provide a Q counterpart.

+Björn Fromén I agree, that sounds plausible to me.

OK, let me attack from a different angle. If the subject of the second verb in the sentence weren't a pronoun but a noun, I feel there would be a difference in meaning between the following sentences:
You have seen the men bear the lords' cloaks. (= you have seen them and they were bearing the cloaks)
You have seen the men bearing the lords' cloaks. (= you have seen the men that were bearing the cloaks [and not some other men]).
Am I right in this?

+Tamas Ferencz You are right. In the original sentence, "them" could only be an object, so there is less ambiguity. By changing the pronoun to "the men", it introduces the possibility that "the men bear the lord's cloaks" is a subordinate clause. In any case, it feels to me that the emphasis is on the verbal action.

In the second sentence, the clause functions more adjectivally, describing the men.

I also think that a similar distinction might appear in Quenya as well, since the infinitive is verbal and the active participle is adjectival.

Thank you, +Paul Strack. I have also noted, that on p118 of PE22, where Tolkien discusses the accusative with infinitive construct, all his examples are ones where the English counterpart uses the to-infinitive (I wished him to come etc.). Also, he states that with verbs that report, say, state facts this construct cannot be used and Q here uses a clause. Could it be that verbs of perception (see, hear, feel) fall into the latter category? (you have seen them bearing the cloaks = you have seen that they were wearing the cloaks)?
Perhaps I am clutching at straws here and it's all very simple and the infinitive should be used; however, I now think that the active participle is not a good solution, unless it actually refers to the main subject of the sentence (you):)

Alright! +Tamas Ferencz, I truly agree agree with you and see the connection with the Parma Eldalamberon 22 and the infinitive. Thank you for your help!