The sea boundary between two states with opposite or adjacent coasts is defined by the median line between baselines realized on shore lines. As defined in UNCLOS (United Nations Convention on the Law of the Sea), every point of the median line must be equidistant from the nearest points on the baselines from which the breadth of the territorialseas of each ofthe two states is measured. The coordinates of breakpoints of the median line are computed based on known coordinates of baseline points on the shores. What is the precision of computed coordinates? Here we study the error propagation on two reference surfaces: (1) plane and (2) sphere. Moreover, four approaches to breakpoint determination are investigated. Algorithms for computation of the covariance matrix of median line breakpoints both on sphere and plane were developed.