In 2004, Ramírez began the year with Columbus. After he had an 0–3 record, an 8.50 ERA, 17 strikeouts, and 18 innings pitched in four starts, he was demoted to Trenton on May 1. On August 17, he allowed just two hits in a 4–1 complete game victory over the Norwich Navigators while setting a team record by retiring the last 24 hitters he faced. With Trenton, Ramírez had a 4–6 record, a 4.62 ERA, two complete games, 128 strikeouts, and 115 innings pitched in 18 starts. His combined minor league totals were a 4–9 record, a 5.14 ERA, two complete games, 145 strikeouts, and 133 innings pitched in 22 starts.