Improving the efficacy of the pilot remotely operated vehicle (ROV) interaction through extensive training is paramount in reducing the duration, and thus expense, of ROV deployments. To complete training without sacrificing operational windows, ROV simulators can be used. Since the ROV tether, which provides power and telemetry, will at times dominate the ROV motion, the tether must be accurately modeled over the full duration of a simulated ROV maneuver. One aspect of the tether dynamics that remains relatively untouched is the modeling of tether self-contact, contact with other tethers, or entanglement. The aim of this work is to present a computationally efficient and accurate method of detecting tether collisions. To this end, a combinatorial global optimization method is first used to determine the approximate separation distance minima locations. Then, a local optimization scheme is used to find the exact separation distances and the locations of the closest points. The first combinatorial stage increases the speed at which the minima can be found. The minimum separation distance information and its change with respect to time can then be used to continuously determine whether a collision has occurred. If a collision is detected, a contact force is calculated from the interference geometry and applied at the collision site.