Methane (CH4) flux to the atmosphere was measured from gas vents and, for the first time, from soil microseepage at four quiescent mud volcanoes and one “everlasting fire” in eastern Azerbaijan. Mud volcanoes show different activity of venting craters, gryphons, and bubbling pools, with CH4 fluxes ranging from less than one to hundreds of tons per year. Microseepage CH4 flux is generally on the order of hundreds of milligrams per square meter per day, even far away from the active centers. The CH4 flux near the everlasting fires (on the order of 105 mg·m−2·d−1) represents the highest natural CH4 emission from soil ever measured. The specific CH4 flux to the atmosphere, between 102 and 103 t·km−2·yr−1, was similar to specific flux from other mud volcanoes in Europe. At least 1400 tons of CH4 per year are released from the investigated areas. It is conservatively estimated that all onshore mud volcanoes of Azerbaijan, during quiescent activity, may still emit ∼0.3–0.9 × 106 t of CH4 per year into the atmosphere. The new data fill a significant gap in the worldwide data set and confirm the importance of geologic sources of greenhouse CH4, although they are not yet considered in the climate-study budgets of atmospheric CH4 sources and sinks.