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Essential tremor (ET) affects millions of people. Although frontline treatment options (medication, deep brain stimulation, and focused ultrasound ablation) have provided significant relief, many patients are unsatisfied with the outcomes. Peripheral suppression techniques, such as injections of botulinum toxin or sensory electrical stimulation of muscles, are gaining popularity, but could be optimized if the muscles most responsible for a patient's tremor were identified. The purpose of this study was to quantify the relationship between the activity in various upper limb muscles and the resulting tremor in patients with ET. Surface electromyogram (sEMG) from the 15 major superficial muscles of the upper limb and displacement of the hand and upper limb joints were recorded from 22 persons with ET while they performed kinetic and postural tasks representative of activities of daily living. We calculated the peak coherence (frequency-dependent correlation) in the tremor band (4-8 Hz) between the sEMG of each muscle and the displacement in each major degree of freedom (DOF). Averaged across subjects with ET, the highest coherence was found between elbow flexors (particularly biceps brachii and brachioradialis) and the distal DOF (forearm, wrist, and hand motion), and between wrist extensors (extensor carpi radialis and ulnaris) and the same distal DOF. These coherence values represent the upper bound on the proportion of the tremor caused by each muscle. We conclude that, without further information, elbow flexors and wrist extensors should be among the first muscles considered for peripheral suppression techniques in persons with ET. NEW & NOTEWORTHY We characterized the relationships between activity in upper limb muscles and tremor in persons with essential tremor using coherence, which provides an upper bound on the proportion of the tremor due to each muscle. Averaged across subjects and various tasks, tremor in the hand and distal joints was most coherent with elbow flexors and wrist extensors. We conclude that, without further information, these muscle groups should be among the first considered for peripheral suppression techniques.