Antique jewelry is often sold ‘as-is’ which means the stones are not removed from their original settings. Therefore, getting an exact carat weight is pretty much impossible. When diamonds are already set, antique jewelers will use a millimeter : weight conversion to calculate an estimated size. The chart below references the measurements of the diamond in millimeters and from there gives you an approximate carat weight.
Keep in mind that these charts apply to diamonds only; modern calibrated cuts. When dealing with older cut stones, it takes more expertise to give an accurate estimate. The girdle thickness, height of crown, and overall depth of the stone can greatly affect carat weight.