Gemara

6b (Rav Sheshes): The primary reward for a eulogy is Deluyei. (This will be explained.)

62a: A eulogizer said in front of Rav Nachman "[the deceased] was very Tzanu'a (modest)."

Rav Nachman: Did you enter the bathroom with him, to see if he was Tzanu'a there?

(Beraisa): One is called Tzanu'a only if he is Tzanu'a in the bathroom.

Question: Why did Rav Nachman care if the deceased was really Tzanu'a or not?

Answer (Beraisa): Just like the deceased are punished, also [false] eulogizers and those who endorse their words are punished.

Shabbos 105b (R. Yehoshua ben Levi): If one sheds tears over a Kosher person, Hash-m counts them and puts them in his treasure-house - "Nodi Sofarta Atah Simah Dim'asi v'Nodecha ha'Lo b'Sifrasecha".

(Rav Yehudah): If one is lazy and neglects to properly eulogize a Kosher person, he should be buried alive. "V'Yikberu (Yehoshua)... mi'Tzafon l'HaR Go'aSH" teaches that he was ROGASH (aroused) the mountain against them to kill them, because he was not eulogized properly.

(R. Chiya bar Aba citing R. Yochanan): If one is lazy and neglects to properly eulogize a Kosher person, he will not live long, Midah k'Neged Midah - "b'Sas'ah (in the same Se'ah (measure)) b'Shalchah Terivenah".

Question (R. Chiya bar Aba): "...Ha'Zekenim Asher He'erichu Yomim Acher Yehoshua" (they lived long)!

Answer (R. Yochanan): (Foolish) Babylonian! They had length of days, but not length of years.

153a (Rav Yehudah brei d'Rav Shmuel): The eulogy indicates whether or not the Mes is a Ben Olam ha'Ba. (It is tearful and laudatory for a Ben Olam ha'Ba.)

Question: If so, why did Rav tell Rav Shmuel bar Shilas 'when I die, strive to eulogize me to arouse people to cry, for I will be there [and I will hear]'? (Surely Rav is a Ben Olam ha'Ba. They will cry in any case!)

Rav Yehudah meant that if people cry when aroused, this shows that the Mes is a Ben Olam ha'Ba. If not, he is not.

Rishonim

Rambam (Hilchos Evel 12:2): If one is lazy and neglects to properly eulogize a Chacham, he will not live long. If one is lazy and neglects to properly eulogize a Kosher Kosher person, it is proper that he be buried alive. If one sheds tears over a Kosher person, Hash-m guards his reward.

Lechem Mishneh: Some texts say that the punishments are for negligence of eulogizing a Chacham. Even though our text learns about not eulogizing a Kosher person from Yehoshua, we must say that the punishment was because he was Kosher. If it was due to his Torah, we could not learn to other Chachamim as famous as Yehoshua!

Rosh (Mo'ed Katan 3:63): When they are praised for merits they did not have at all, this arouses judgment against them). Also [false] eulogizers and those who endorse their words are punished.

Rashi (105b DH Midah): Since he (the negligent eulogizer) did not mourn over the shortened life of the Mes, Shamayim will not be concerned for [shortening of] his life.

Poskim

Shulchan Aruch (YD 344:1): It is a great Mitzvah to properly eulogize the Mes. The Mitzvah is to raise one's voice and say things that humble the heart, to increase crying and mention the Mes' praise. One may not exaggerate his praise too much. Rather, we mention his good Midos, and add a little, just one does not overdo it. If he did not have good Midos at all, he does not mention about him. A Chacham and a Chasid, we mention their Chachmah and Chasidus. One who mentions things that were not in the Mes at all, or exaggerates too much about what he had, causes Misah to himself and the Mes.

Beis Yosef (DH u'Mitzvaso): The primary reward for a eulogy is Deluyei. The Ramban explains that this is raising one's voice in eulogizing Chachamim and Kesherim. The Yerushalmi learns from "He'anek Dom" (which was a Hora'as Sha'ah, i.e. a special temporary ruling, that Yechezkeil be quiet), that normally one must shout about the dead.

Beis Yosef (DH v'Asur): The Ramban (Toras ha'Adam p.82) brings from Evel Rabsi that we do not add at the beginning, but we add to the Ikar. I.e. we do not honorably eulogize someone not proper for this at the time of the eulogy, but if he deserved some honor, we extend this and add a little to his praise.

Beis Yosef (DH v'Ha): The Aruch explains that just like the deceased is punished if he sinned, also eulogizers who said that he was a Tzadik are punished. This connotes that the Mes is not punished for attributes he was falsely credited with.

Beis Yosef (DH Kasav): The Ramban says that one may not exaggerate the praise of the deceased more than what was seen in him. Rather, we praise him according to his honor, and a little more, like people normally praise. One may not exaggerate excessively. If he is not worthy of this, we eulogize like the women of Shachnetziv (Mo'ed Katan 28b) who say 'all die alike (i.e. rich or poor). This man suffered greatly.' They said so because he was not worthy of another eulogy.

Bach (2): Because it is forbidden to diminish the praise of the Mes, they permitted to add slightly to his praise. If it were forbidden to add, perhaps Chas v'Shalom people would come to detract. To exaggerate excessively is surely forbidden, or to praise for a matter he did not have at all. This arouses the detriment of the Mes, and he is punished for not having the trait for which he is praised! There is no need to teach that the eulogizers will be punished for Sheker and flattering one who is not a Tzadik, to say that he is a Tzadik.

Taz (1): What is the difference between a little Sheker and much Sheker? It seems that everyone who does a Mitzvah, e.g. gives a certain amount of Tzedakah, surely had there been a slightly bigger need, he would not have refrained from doing it. Therefore, it is considered as if he did it, so it is not Sheker. The Yerushalmi says that the Mes knows and hears his praise, like amidst a dream, and he knows everything they say in front of him until the coffin is covered.

Birkei Yosef (1): We may add a little because presumably, people did not know the extent of his Midos. Since he had good Midos, surely some of them were not publicized, either because he intentionally concealed them, or because people are not so meticulous to know that the perfection of all good Midos. However, it is permitted to add only a little.

Birkei Yosef (2): All the more so it is forbidden if it disgraces previous Mesim, who were great Rabanan and these praiseworthy things were not said about them. If the eulogy blemishes the honor of living Chachamim, for it [falsely] says that the Mes was greater than them, they may excommunicate the eulogizer, like the case of Yehudah ben Kenusa, (Yehudah was being stringent to avoid obstacles on the road, even though Yehoshua's stipulation permits walking over them. R. Chiya said that if not that he knew that all Yehudah's acts are l'Shem Shamayim, he would have excommunicated him.) If the Mes is equated to previous Chachamim, one may be lenient, for Yiftach (an ignorant leader) in his generation (is like Shmuel in his generation - Rosh Hashanah 25b). Everything depends on the situation.

Einayim l'Mishpat (62a:8): Margenisa d'R. Meir says 'woe to one who people err about (think that he is greater than he truly is). Also the eulogizers are punished, for they contribute to this. Sometimes Chilul Hash-m results!' Hash-m Himself punishes one who falsely shows himself to be a Tzadik (Koheles Rabah 4:1). If one who is not a Chacham wears the Talis of a Chacham (he does not enter Hash-m's place - Bava Basra 98a).