Muzio Tedaldi was a friend and "godfather" to Vincenzo Galilei (c.1520-1591).

Even before they became related, Tedaldi was so close to the Galilei family that he would look after Vincenzo's wife and daughters during his long work absences.

In the period when Vincenzo lived in Florence, while the rest of the family stayed in Pisa, Muzio Tedaldi would see to all matters concerning the schooling of the little Galilei children, as is noted in letters and account books.

On December 21, 1575 he became godfather to Michelangelo at his baptism. In 1578 he married Bartolomea Ammannati, Galileo's cousin on his mother's side.