Constrained by production capacity and the pressure to reduce emissions, many original equipment manufacturers (OEMs) authorize third-party remanufacturers (TPRs) to remanufacture patented products. We investigate the operational decisions of OEMs and authorized TPRs under carbon cap-and-trade regulations in a two-echelon supply chain. We first formulate an operational decision model for OEMs before a TPR enters. Then, for the cases of centralized and decentralized decision making, we formulate an operational decision-making model for the TPR and, subsequently, establish one for the OEM after the TPR enters. We further analyze the effects of carbon emissions cap, trading price of carbon permits, yield rate, and consumer willingness to pay (WTP) on optimal decisions. Our results indicate: whether TPRs accept authorization remanufacturing depending on the ratio of carbon emissions cap to carbon emissions for producing per remanufactured product; royalty rate is negatively affected by trading price of carbon permits and per remanufactured product’ carbon emissions other than that for per new product, and can offset the threat caused by TPRs; the implementation of carbon cap-and-trade regulations causes OEMs to charge TPRs lower royalty rate; centralized decision making increases the total profit of the supply chain and delivers superior environmental benefits. As yield rate and WTP increase, the total profit increases, increasingly sensitive to WTP.