Are there any extant samples of the native Celtic languages spoken in Britain when it was under Roman rule? In other words, what would the language of Boudica or Caractacus have sounded like? I am familiar with the historical texts on Britain by Roman writers including Tacitus (He describes Boudica and Caractacus in his Annals, for example), Dio Cassius, and Julius Caesar (the first invasion of Britain). All of those texts on Roman Britain that I know of are in Latin, but are there any truly authentic sources for the Celtic language spoken around the first century AD in Britain? I have not been able to find any such sources thus far.
The Celtic languages of Roman Britain were almost never written down in ancient times, so most of our clues about how Boudica or Caractacus spoke come from using the comparative method of historical linguistics. The Celtic family had two branches, Continental (spoken in Europe) and Insular (spoken in Britain, includes all the modern Celtic languages). Insular Celtic is divided into Goidelic and Brythonic; the latter was spoken in Roman Britain and is the approximate ancestor of Welsh, Breton, and Cornish. We can look at ancient attestations of Continental Celtic, and we can look at Insular Celtic as attested from the 5th century on.
For ancient Brythonic itself, we have little bits of evidence. Besides a couple coins with the names of pre-Roman kings, there are lots of Celtic personal names and place names in Greek and Latin sources: Ptolemy's Geography, official Roman geographical documents, and a list of people in the Roman forces. Those proper nouns allow us to derive some information about the language, because they often have roots recognizable from other Celtic and Indo-European words.
The other evidence for Brythonic in the Roman period is two inscriptions from Bath. There are some factors that help our potential understanding of them: they're written in Latin script, and we can reasonably guess from archaeological context and form that they are curse tablets, comparable to many Latin curse tablets from the same site. But there are also problems: they are short, and one of them is fragmentary, and they are in a language that isn't fully attested. For example, one of the two looks like this:
adixoui / deiana (or deuina) / deieda (or deueda) / andagin / uindiorix / cuamiin / ai
You can read one interpretation of what this means in the article I've linked below; the author suggests that the meaning is something like "I, Vindiorix, o goddess Deveda, will affix an evil (fate) on Cuamiina." Still, it's a bit speculative and definitely still open to debate; almost every word in that short inscription has been interpreted different ways by different linguists, and there have been some people who said these might actually be in a Continental Celtic language, mostly because Continental Celtic was frequently written in this period and, other than the Bath tablets, Insular Celtic wasn't. If we unearth more inscriptions in the coming decades and have more data to work with, it's entirely possible that we'll get a different and better understanding of these texts.
(edit: typos)
Sources
Jackson 1953 Language and history in early Britain
Fortson 2009, Indo-European language and culture
Mullen 2007, "Evidence for written Celtic from Roman Britain: a linguistic analysis of Tabellae Sulis 14 and 18" in Studia Celtica