Conservative mapping of data from one horizontal grid to another should preserve certain integral or mean properties of the original data. This may be essential in some model applications, including ensuring realistic exchange of energy and mass between coupled model components. It can also be essential for certain types of analysis, such as evaluating how far a system is from an equilibrium state. For some common grids, existing remapping algorithms may fail to perfectly represent the shapes and sizes of grid cells, which leads to errors in the remapped fields. A procedure is presented here that enables users to rely on the mapping weights generated by remapping algorithms but corrects for their deficiencies. With this procedure, for a given pair of source and destination grids, a single set of remapping weights can be applied to remap any variable, including those with grid cells that are partially or fully masked.