Incompetence rhymes with:
impotence, impotence, omnipotence, capacitance, impotence, inheritance, omnipotence, acceptance, acquaintance, admittance, assistance, capacitance, coexistence, consistence, constance, distance, existence, importance, impotence, inadvertence, inductance, inheritance, insistence, instance, omnipotence, outdistance, persistence, pittance, quaintance, reluctance, remittance, repentance, resistance, resistence, self-subsistence, sentence, subsistence, substance