I've just got to get this out there, after seeing so many people make terrible assumptions about what rhymes can tell you about the English pronunciation of the past.
Did pre-modern English poets' verse always rhyme perfectly in their own speech?
Not so much. No. They didn't in the 16th century. They didn't in the 17th. Nor at any later point.
This becomes obvious when we get the rare chance to see a poem phonetically transcribed (or in this case, notated) by its author.
Here's the verse preface to Hodges' "English primrose" (1644) with his phonetic diacritics.
Some of these rhymes which would be imperfect in modern English clearly are perfect. For example rare/are (both resting, it appears, on /æ:r/). Likewise gave/have (resting on /æ:v/). But note the rhyme of forth/worth. Based on Hodges' diacritics, these would be /fo:rθ/ and /wʌrθ/. Even less perfect rhymes for Hodges than they are for me!
Were there varieties of English in which forth/worth was a perfect rhyme? Absolutely, yes. In the dialects reported by John Hart and William Bullokar in the previous century these were /furθ/ and /wurθ/. Were there still speakers who had identical vowels in both? Probably. Descendants of /furθ/ survive today in southern England, albeit not in RP. Did Hodges feel the need to dip into their lect for the actual pronunciation of his rhymes? Apparently not.
Another author of verse from the period who transcribed some of his own verse was the phonetician Robert Robinson (fl 1617). In a poem of his own composition, he rhymes what/that and prove/dove for which he transcribes <w̥ot>, <ðat>, <pruwv>, <duv> (using Dobson's system for transliterating Robinson's phonetic symbols), amounting most probably to /ʍɔt/, /ðat/, /pru:v/, /dʊv/.
Did forms of speech exist in which these would have been perfect rhymes? Again, yes. We have explicit evidence for a pronunciation of "what" with an unrounded vowel also existing within Robinson's own time and after. In fact, not only is he unusual (as a source from the early 17th century) in recording a rounded vowel here but he is the first to do so. All of his contemporaries (Gil, Hodges) record their TRAP vowel in this word. The nature of Robinson's evidence suggests rounding of ME /wă/ began in weakly-stressed environments, which explains why it is mostly limited to function words for him (though he transcribes a rounded vowel once in "want", besides five instances of the unrounded form, and also once in "warrant"). So it is admittedly just possible that Robinson by force of habit forgot to transcribe an unrounded marked strong form under stress at the rhyme here. This rhyme might deserve an asterisk, as it is conceivable (but only just) that Robinson's pronunciation might have had identical vowels for both words in this environment.
There can be no such doubt about prove/dove, however, where Robinson's rhymes are clearly either traditional or resting on a pronunciation (either a short vowel in the first word, or a long one in the second) other than his own speech. Versions of "prove" with a short vowel are attested securely but rarely by other sources, and mostly in the preceding century, though at least one contemporary of Robinson's (Thomas Tonkis) reports it. It may be that the long vowel in "prove" and "move" was sustained as a learned form, current among the learned men who produced our evidence, but there can be no doubt that a long vowel is what obtained in Robinson's speech; he transcribes "prove" nine times and "move" six times, and always with a long vowel. Versions of "dove" with a long vowel are attested, but in the 16th century only, and then rarely (though that may just be because it's not as commonly transcribed as some other words like "love".) It's unlikely this was a common pronunciation in Robinson's London, and there's no reason at all to think his own pronunciation was anything other than what his transcription implies.
Now, there is evidence that people in reciting verse might adjust their normal pronunciation to a degree to give full rhymes. For example, the only time Robinson transcribes secondarily stressed final <-y> with /i:/ is when rhyme requires it, e.g. misery/she. Alexander Gil's transcriptions of Spenser show that when rhyme called for it he could adopt pronunciations of head (rhyming with lead v.b.), desert, swerve (rhyming with art, starve), dear (rhyming with were), and poor, door (rhyming with store, adore) other than his normal one.
But this kind of thing only went so far. Gil's transcriptions in particular do not accomodate rhymes that rest on a pronunciation used by social groups he found objectionable: thus he transcribes Spenser's rhyme despair/whilere as <despair>/<whjl-ēr> (the rhymes rests on a monophthongized WAIT vowel which Gil condemned with mighty spleen as an effete affectation). Mismatches in shortening of ME /ọ̄/ do not affect his transcriptions at rhyme. Wood/stood and move/love are for him <wud>/<stūd> and <mūv>/<luv>. Nor does he drop the velar fricative in "fight" when Spenser rhymes this word with "smite". Recitation practice (as one might expect) also seems like it varied considerably from person to person. (In Robinson's transcriptions of his own verse, the two examples I cited are the only imperfect rhymes, but his transcriptions of Richard Barnfield's verse are on the whole remarkable for how unconcerned with rhyme they are: he often opts to transcribe a non-rhyming form even when the form that would've made a perfect rhyme also existed in his own speech.)
And, as I've just shown, poets themselves could clearly rely for their rhymes on forms of speech other than their own. My point is that one cannot assume, without a good deal of other evidence, that a pre-modern poet's use of a particular rhyme implies that the pronunciation on which such a rhyme rests was necessarily their own. It doesn't even necessarily imply that the rhyme would have been perfect in their own reading of their own verse.
Much more evidence than mere use of a rhyme is required.
For example, that Shakespeare rhymes build only ever with shield, field, yield and never once with a word like "killed" may in fact give one reason to suspect that he himself used a version of the word with the MEET vowel (explicitly attested as a variant by Shakespeare's contemporaries.) But the fact that he once rhymes the infinitive of read with dead tells us only what we know from other evidence (that there existed forms of speech where read and dead could both have the MEAT vowel), and nothing at all Shakespeare's speech. A single rhyme like Shakespeare's groin/swine with no other rhymes implying merger of ME /ui oi/ with that of ME /ī/ tells us at most only that such a pronunciation existed (and may in fact mean nothing at all as groin could have a pronunciation grine which would be etymologically expected). On the other hand, the fact that Shakespeare — outside this one ambiguous example — so conspicuously avoids rhyming ME /ui/ with ME /ī/ (rhymes like toil/mile exist in some of his contemporaries, but are absent in his work) may actually tell us more, at least about his rhyming-sensibilities if not about what his own speech was like.
Poets also could and did also use what are unarguably approximate rhymes, like Spenser's sharpe/darke, gather/scater. But many seem to routinely forget this, especially when it comes to Shakespeare (despite his use of rhymes like open/broken, come/sung), reluctant accept that a given rhyme might well not rest on phonetic identity. Ellis, Kökeritz and David Crystal would have one believe that Shakespeare must have pronounced nothing as a perfect rhyme for doting on the strength of one solitary rhyme and a couple of dubious puns, for example. That modern "OP" performances are full of actors saying /no:tɪn/ for every. single. instance of this word in Shakespeare's scripts (the only form supplied in Crystal's "Dictionary of Original Shakespearean Pronunciation") is a testament to the weirdness of Anglo ideologies concerning Shakespeare and his language. Ideologies can make people miss the obvious: in this case, the fact that — because of how sound-changes had shaken out — the word "nothing" will have had few if any perfect rhymes. The segment /θ/ did not normally occur in this environment, apart from loanwords (mostly from Greek, where final /ŋ/ was phonotactically impermissible). A poet wishing to rhyme on nothing would have to adapt, either by using a word with a voiced interdental (as in Drayton's nothing/loathing) or do what Shakespeare did and rhyme on /t/.
What I wouldn't give to see people cease their irresponsible use of rhyme.
No pre-modern literary text was ever written with a future philologist audience in mind, and don't you forget it.
Ok, there, here endeth the ramble
