The maximum resolution for Port Royale 3 can be set to 1920 x 1200. But if required you can even go higher.
Simply open

%appdata%Kalypso Mediaoptions.cfg

and enter a higher resolution, you have to active the window mode!

After you started the game, you have to press the maximize-button of the window, now you should be able to run the game with a higher resolution.

The file options.cfg can be opened and edited with notepad or any other editor.

Set the file to “view only” after the changes, Port Royale 3 might reset your changes elsewise.