Cygwin
1.) sig-win ('sɪɡwɪn)
This is pretty well established.
MinGW
Less have I come across this, but if you were to come across it for whatever reason (a talk or presentation for some sort of type-con, for example) I would advise this:
I would accept either:
1.) Ming Win ('miːŋɡwɪn)
2.) Mihn Jee Win ('mɪndʒiːwɪn)
3.) Mihn Jee Wee (mɪn'dʒiːwiː)
However, I would discourage:
1.) Ming Double-U (miːŋɡ'dʌbljuː)
Much too difficult to say.
If ever coming across MinGW in a verbal setting, it would be advised to have it written out also.