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The study was conducted to determine appropriate numbers and times of daily gas measurements to estimate total daily methane (CH4) emission of meat goats using a GreenFeed system (GFS). A replicated 4 (four measurement protocols) × 4 (four periods) Latin square design was employed with 16 Boer wethers in a confinement pen setting. Measurement protocols entailed three (G-3T; 0600–0700, 1400–1500, and 2200–2300 h), four (G-4T; 0700–0800, 1300–1400, 1900–2000, and 0100–0200 h), and six (G-6T; 0800–0900, 1200–1300, 1600–1700, 2000–2100, 0000–0100, and 0400–0500 h) times for daily measurement periods in GFS. The fourth protocol was continuous measurement over 24 h with animals in an open-circuit respiration calorimetry system (CS). Oat hay was given in individual feeders, and a small predetermined quantity of a pelleted concentrate supplement (bait) was dispensed by the GFS or manually offered for the CS. Overall, total dry matter (DM) intake (614, 625, 635, and 577 g/day for CS, G-3T, G-4T, and G-6T, respectively; SEM = 13.9) and digestible DM intake (359, 368, 374, and 320 CS, G-3T, G-4T, and G-6T, respectively; SEM = 15.9) were lower for CS than for G-3T, G-4T, and G-6T (p < 0.05), but these variables were not different among the GFS protocols. There was a significant (p < 0.001) effect of measurement protocol on CH4 emission in g/day (11.1, 25.6, 27.3, and 26.7 for CS, G-3T, G-4T, and G-6T, respectively; SEM = 1.11), g/kg DM intake (19.3, 46.4, 43.9, and 42.4 for CS, G-3T, G-4T, and G-6T, respectively; SEM = 2.03), and g/kg body weight (0.49, 1.11, 1.18, and 1.16 for CS, G-3T, G-4T, and G-6T, respectively; SEM = 0.052), with values being much lower for CS than for G-3T, G-4T and G-6T. Conversely, CH4 emission was similar among the GFS protocols despite differences in the time and number of daily visits (2.03, 2.76, and 3.75 visits for G-3T, G-4T, and G-6T, respectively; SEM = 0.114; p < 0.001). Pearson correlation (r) analysis indicated a moderate to high (p < 0.05) correlation between CS and G-3T (r = 0.62 for CH4 in g/day and r = 0.59 for CH4 in g/kg BW), CS and G-4T (r = 0.67 for CH4 in g/day and r = 0.76 for CH4 in g/kg BW), and CS and G-6T (r = 0.70 for CH4 in g/day and r = 0.75 for CH4 in g/kg BW). However, the correlation coefficient for CH4 in g/kg DM intake was low between CS and G-3T (r = 0.11) and CS and G-6T (r = 0.31) but slightly greater between CS and G-4T (r = 0.47). In conclusion, the results suggest that CH4 emissions using GFS in a confinement setting were greater compared with the CS in goats, but CH4-emission estimation using the GFS correlated with the CH4 emission in the CS system with a stronger relationship for the four times of daily measurements.