The world during the COVID-19 pandemic has led to extensive use of virtual activities by means of electronic devices, which are made up of rare earth elements (REEs). This means that quantitative knowledge of REEs in various resources is crucial for the development of effective recovery methods. Therefore, this report describes a simple microwave assisted ashing followed by ultrasound-assisted extraction (MAA-UAE) for quantitative determination of REEs in coal samples using inductively coupled plasma-optical emission spectroscopy (ICP-OES). Firstly, coal samples were ashed at 55 °C for 4.5 h to form white ashes, which were then treated with dilute HNO3 acid under ultrasonication to enhance the extraction of REEs. The quantitative recoveries (86–120%) of REEs were obtained when 1 mol L−1, 0.1 g, 40 °C, 20 min, and high frequency were applied for [HNO3], sample mass, ultrasonic bath temperature, extraction time, and ultrasonic bath frequency, respectively. The method detection limits of the proposed MAA-UAE method were between 0.0075 and 0.59 µg g−1 with satisfactory precision (<5%). The concentration levels of REEs in South African coals ranged from 1.4 to 105 µg g−1, suggesting that this coal can be a resource for REEs.