An objective analysis technique is described which permits an extrapolation, over the entire basin, of amplitudes and phases of the tidal height field given at a few locations in the basin. The method depends on expansion of the tidal height field in terms of a set of orthogonal functions that are characteristic of the given ocean or lake basin. These functions take into account the bottom topography, the horizontal plan form of the basin, and the necessary boundary conditions. They are determined numerically as solutions of a self-adjoint elliptic differential equation. Given tidal data at n random locations in a basin, one can then determine a number of expansion coefficients ≤n by a linear least-squares procedure. Since the basis functions are known over the whole basin, one can recover the tidal amplitudes and phases over the entire basin. As a test case, the method was applied to determine the M₂ tide in Lake Superior. A comparison of tidal amplitudes and phases determined from a theoretical simulation with those obtained from the objective analysis using the theoretical data at a few points shows excellent agreement. In addition, the theoretically simulated amplitudes and phases of the M₂ tidal height field agree very well with those obtained from analysis of the hourly water level data available at ten stations around the lake boundary.