@ClearBlueWater - there is a whole body of study devoted to how Shakespeare's actors would have pronounced things, which is a slightly different question to how he would have pronounced things. However, Jay-kweez/Jaykz is one of the ones that without doubt because of the metre, rhyme, jokes, and other texts of the time with similar pronunciation.
That's why we know the pronunciation of Jaykweez - it's a result of scholarship, not guesswork.
Same with glams; someone above said it was possibly actually pronounced glamis. That is probably based on a bad quarto - basically early literary pirates going writing down what they think was said on stage and then selling it on to the public who were clamouring for a Shakespeare text they could reenact at home. If you're interested, try reading the bad quarto version of to be or not to be.
The second folio (and, actually, one of the bad quartos) makes it clear that the accepted pronunciation was either glaamz or glamz, but not glamis. Shakespeare didn't write this either - none of his scripts are extant - but it was written and published by people he knew well who also knew the plays well rather than some chancer selling stuff quickly out the back door.
Not all of the words in Shakespeare where their pronunciation is unclear have such solid scholarship behind them, but these two (Jaykweez and Glaamz) do.