The process of anthracite and its semi-coke combustion in the presence of 5 wt.% (in terms of dry salt) additives of copper salts Cu(NO3)2 and Cu(CH3COO)2 was studied. The activating additives were introduced by an incipient wetness procedure. The ignition and combustion parameters for coal samples were examined in the combustion chamber at the heating medium temperatures (Tg) of 600–800 °C. The composition of the gaseous combustion products was controlled using an on-line gas analyzer. The fuel modification with copper salts was found to reduce the ignition delay time on average, along with a drop in the minimum ignition temperature Tmin by 138–277 °C. With an increase in Tg temperature, a significant reduction in the ignition delay time for the anthracite and semi-coke samples (by a factor of 6.7) was observed. The maximum difference in the ignition delay time between the original and modified samples of anthracite (ΔTi = 5.5 s) and semi-coke (ΔTi = 5.4 s) was recorded at a Tg temperature of 600 °C in the case of Cu(CH3COO)2. The emergence of micro-explosions was detected at an early stage of combustion via high-speed video imaging for samples modified by copper acetate. According to the on-line gas analysis data, the addition of copper salts permits one to reduce the volume of CO formed by 40% on average, providing complete oxidation of the fuel to CO2. It was shown that the introduction of additives promoted the reduction in the NOx emissions during the combustion of the anthracite and semi-coke samples.