I asked this question one year ago. Nico gave an excellent answer, but I still have some confusion.
A: We saw a police helicopter overhead yesterday morning.
B: Really? They would have been looking for those bank robbers.
As Nico mentioned in his comments, in the original context, only "would have been looking for.." applies, because the use of "we saw..." (simple past) implies that the search is also in the past and doesn't extend to the present (at least in BrE). Whereas "will have been looking for.." suggests the search extends to the present or is relevant at present.
Besides, he pointed out that in the OP's example, B isn't pretty sure, B isn't expressing certainty. Note that B starts the sentence with "Really?". B is expressing a belief. B believes that the police had been looking for those bank robbers.
I suspect "They will have been looking for those bank robbers" applies to the context as well.
My main argument is taken from F. R. Palmer's Modality and the English Modals:
Generally the modality is in the present only, because the judgments are made in the act of speaking, epistemic modals being in this sense usually 'performative'. The modal verbs are not normally used, therefore, in past tense forms to refer to past judgments. Past tense forms are normally tentative with present time reference. It is, of course, possible to report past judgments, but this requires verbs such as THINK, BELIEVE, etc.
Based on this, I think "They will have been looking for those bank robbers yesterday" is a grammatical sentence, meaning "I'm sure they were looking for those bank robbers yesterday". Is my understanding correct?
This use doesn't seem to be very productive. I got a couple examples from the Internet:
In terms of the GC Contador, Uran and Aru will have been relatively happy with their rides yesterday. Contador's team in fact led at the intermediate time check at 9.9km but lost ground - and their leader briefly - and had to settle for second place on the stage.
I don't know if they are standard English or regional variations. Even the present perfect can sometimes be used together with expressions of finished time, but we know that's not standard English.