Just to clarify your statement, Milton visited Galileo whilst Galileo was under house arrest. When he was a young man Milton made a "Grand Tour" (though it probably wasn't called that for another century or so) through Italy, and (naturally) impressed everyone important with his erudition.

Milton's encounter with Galileo left an impression, as his case is given as an important example of the importance of free (even "heretical") speech in Aeropagetica.