As other comments have indicated, in Classical Latin there seem to have been few or no examples of heterographic homophones of the kind that are found in English (with two separate words, e.g. meet and meat, which have different meanings and consistently different spellings, but consistently identical pronunciations in standard dialects).
Latin of any period definitely has homographic homophones, and Classical Latin had a number of heterophonic homographs (mainly because of the practice of writing long and short vowels the same way), but neither of those are relevant to your question.
Draconis's answer provides examples of what I think are the closest we can get in most cases to heterographic homophones: words that had spelling variants that weren't associated with different meanings or different pronunciations (as far as we can tell). As Alex B. said in a comment, these would not actually be classified as "homophones". (I've posted an ELU question asking for a word or term to describe words with spelling variants.)
Certain variant spellings unrelated to pronunciation in Classical Latin
In addition to the spelling variants that Draconis mentioned, here are some others that show up in Classical Latin:
C = K: The letter K was infrequent in Classical Latin, but it was used in the word Kalendae and the place name Karthago. These had alternative spellings with C, Calendae and Carthago. Both letters represented the same sound, the velar plosive /k/.
M = N: Coda nasal consonants in Latin typically had the same place of articulation as a following plosive (the only reason I say "typically" is because I'm not quite sure about the usual phonological analysis of the consonant cluster found in emptus and related words, where the p is diachronically/morphologically epenthetic, and I believe sometimes not written). Regressive place assimilation of a nasal within a word was sometimes marked in writing, and sometimes not, but I don't think this variation in spelling is believed to have had a perfect correspondence to any analogous variation in pronunciation. An example of a word which had two spelling variants with M and N is quamquam/quanquam (my understanding is that this word is thought to have been pronounced with a velar nasal [ŋ], regardless of the spelling).
X = XS → S = 1: When a word starting with S was prefixed with ex-, the S might or might not be omitted. Even if there was some variation in pronunciation between the use of /ks.s/ and /k.s/ in such words (I don't know if there was, and I'm not sure how we could determine this), I doubt that the spelling variation had any kind of consistent correspondence to a possible difference in pronunciation. An example is exsisto/existo.
More old-fashioned (?) examples
There are a number of other spelling variants in Latin that I can think of, but that I think are less often seen. I have the impression that they came to be old-fashioned even in the time of Classical Latin.
II = I → I = 1: in medial position between vowels, it is thought that the single letter I could represent the geminate palatal approximant [j.j] in Classical Latin. An alternative representation of this sound was II. In Vox Latina, W. Sidney Allen says that inscriptions show spellings like
PompeIius, cuiIus, eiius, maiIorem for Pompeius, cuius, eius, maiorem, and says that "Quintilian and other grammarians [...] tell us that Cicero and Caesar used in fact to spell such words [as aio, maior, peior, Troia] with ii" (p. 39).
EI = I → E = 1: I know that in some time periods, the digraph EI was used as a variant of I (I think only when I was a long vowel). In Old Latin, EI is thought to have represented a distinct sound from both E and I, but Old Latin EI ended up merging with long I, which caused both spellings to be used for the same sound. This led to variation between I and EI in the spellings of various words pronounced with the long I sound [iː].
If we accept both of these, then we have S H E I all equal to 1.
Less certain examples
If we look at post-Classical periods, there are many more identities that could probably be established (although I haven't looked for examples of homophones). The value of the digraphs ae and oe merged early on with the value of the single letter e (although this also contributed to variability and instability in the spelling of individual words). In certain varieties of Latin, ti and ci came to have the same value (something like [tsj]) in certain contexts.
For some spellings, it's a bit unclear when they first came to represent identical pronunciations. Word-final m in Latin is known to have been subject to elision from early on (especially when it came before a vowel); some scholars believe that Classical Latin had distinctive nasalization of a vowel preceding word-final M, even if the nasal consonant was lost, but as far as I know we don't have that much evidence of this. Except for in monosyllables, all nasality has been lost in descendants of Latin. I guess this could be used as a basis for assigning the value "1" to M, based on multi-word equivalences like libra aut = libram aut.
Latin also had a number of assimilations that might or might not be written. For example, N at the end of a prefix, as in con- and in-, could assimilate to a following L or R, and D at the end of the prefix ad- could assimilate to most other consonants.
I found a relevant passage in Reading in Medieval St. Gall, by Anna A. Grotans (2006). Grotans says that in Isidore's Etymologiae (from the late sixth and seventh centuries), the words ad (preposition) and at (conjunction) are given as an example of heterographic homophones (p. 295).