Well... there are several people who were connected with Michelangelo romantically. But he never married. Michelangelo was a poet as well as all his other accomplishments. The largest number of works written by him were dedicated to Tomaso dei Cavalieri.
In his later years he also had a written relationship with a noble woman named Vittoria Colonna, a poet, in which they exchanged sonnets and letters.
All of his relationships could well have been platonic because he supposedly practiced "monk-like chastity" according to one historian. It is possible that all of his passion was poured into his art. He is also reported to have lived very frugally, even to the point of poverty, though he was able to afford much better.
Michelangelo is known so much more for his work and was a more private person with regard to his non-work life so it's hard to know for sure.
I hope this answers your question.