Can't speak of most of ancient linguistic representation, but it got several modern classifications...maybe wrong, at least using debated (and debatable) groupings.
I would guess that the main problem is that when you're talking about closely related, neighboring languages that have diverged less than 1,000 years ago, a phylogenic tree becomes less and less useful as a way of representing them.
Deducing the "correct" configuration of a linguistic phylogenetic tree is constantly hampered by the other great process of language change, language contact. In fact, over the last 50 years, the field has been moving away from the linear Stammbaum model first adopted by the Neo-Grammarians in the 19th century, and towards a sort of "Wave" model, where genetic provenance and areal contact are simultaneously modeled and accounted for, and one speaks more of particular typological traits and lexical material spreading across geographic areas, rather than a familial tree of proto-languages iteratively dividing, cell-like, into daughter languages.
As my research area is focused on American Indian languages, I'll provide an example from this region, though it applies equally to many of the problems with the internal classification of Indo-European.
In the central Andes, two large linguistic assemblages are found: Quechuan and Aymaran. The Quechuan language family was historically the majority speech of Tawantinsuyu, but has a long history in the Andean region. Much like Arabic and Chinese, Quechua is a group of closely-related and variously-differentiated languages, rather than a single language. The Aymaran language family, concentrated in the Altiplano region around Lake Titicaca, likewise has a long history (it may have been present at Tiwanaku, and was likely the speach of the pre-Inca Huari (Wari) civilization) but today is represented by only two varieties - Aymara proper, with several million speakers in the Altiplano, and Jaqaru, a small village language found in the Lima region of central Peru.
Comparing these two linguistic assemblages using the same processes that were used to model Indo-European, we run up against a large amount of conflicting evidence for whether these two families are genetically related or only similar due to contact.
Firstly, the morphosyntax of the two famillies is virtually identical, to the extent that it's quite easy to take a Quechua sentence, replace all the words and morphemes with Aymara equivalents (or vice-versa) without changing the order of even a single element, and then read the same sentence back, and it will have a completely intelligible meaning to the relevant speaker. As the syntactic type found in the families is a dominant one worldwide (head-final and SOV), this could be due partially to structural entropy, but is certainly also partially due to intense and prolonged contact effects.
Secondly, the phonology of the two families is very similar - their phoneme inventories are nearly identical, for example - but there are a few telling differences. For example, ejective and aspirated stop series within Quechua are principally found among those varieties that historically or currently are in contact with Aymara, suggesting these phonological traits diffused from Aymara into Quechua. Additionally, Aymara is characterized by a complex process of "vowel suppression", wherein the deletion of vowels is triggered by specific morphological processes, a feature that is almost completely alien to Quechua. This mixture of similarities and differences suggests either that a) both started out with identical phoneme systems, suggesting common genetic origin, but at some point each came under different outside influences, or b), the opposite, that each started with different phoneme systems but came to resemble each other (incompletely) over a period of prolonged contact (I favor this hypothesis).
Lastly, and most interestingly, is the lexicon (vocabulary) of the two families. In Indo-European languages, there are large numbers of lexemes reconstructible to the proto-language that have undergone regular sound changes in different branches, but that are still obviously (to the specialist anway) derived from the same root. Examples include
wheel - kyklos - chakra (Germanic-Greek-Indic),
fish - iasc - piscis (Germanic - Celtic - Italic), or
brother - brat' - barâdar (Germanic - Slavic - Iranian), to cite just a few. But in Quechua and Aymara, the vast majority of lexical comparisons yield either zero common roots (even taking into account obscure correspondences), or complete identity. Examples of the former include Quechua
runa, Aymara
jaqi "human, person, people", Q.
yaku, A.
uma "water", Q.
iskay, A.
paya "two", and Q.
maki, A.
ampara "hand". Examples of the latter include Q./A.
warmi "woman, wife", Q./A.
nina "fire", Q./A.
challwa "fish", Q./A.
inti "sun". The number of sound-shifted ancient cognates, of the type commonly found between Indo-European groups, is quite small for Quechua and Aymara - e.g. dialectal Q.
unu and A.
uma for "water" - and may just as easily represent an ancient borrowing as it can evidence for genetic relationship. So on the whole, the relationship between the lexicons of Quechua and Aymara is very different from the relationship between the lexicons of the branches of Indo-European - either there's no similarities, or there's complete identity, which points to a period of recent contact preceded by a long period of separate development, though many linguists have still been tempted to classify them as genetically related in some way at the earliest level.
These kinds of ambiguities are not limited to the Americas, however; they're common in many parts of the world. In Eurasia, the "Altaic" family provides a good example - there is still no real consensus on whether the Turkic, Mongolic, and Tungusic languages stem from a single ancestral proto-language, or came to resemble each other through long periods of mutual contact due to shared culture and political organization (likewise for whether Korean and Japanese belong with this group, or even with each other). Fortunately, though, the trend in the field has been to consider both functions as part of the phylogeny of a language, so the question of whether Quechua and Aymara, or Mongolian and Turkish, are "related" in the Neo-Grammarian/Indo-European sense may no longer be relevant.
Apologies for the long post, just thought I'd clarify some of these issues surrounding language classification and phylogeny.