To force the game to run at a set resolution follow the steps below:
To change the resolution to a custom resolution you need to edit the ini file for the game.
Browse to the installation directory (C:\program files\Firaxis games\Sid Meier's Civilization 4 by default)
Double click on the file named _Civ4Config
Browse through the file for the line:
Screenheight = 0
Screenwidth = 0
You need to change these values to the ones you wish and save the file. For example, changing the settings to:
Screenheight = 1024
Screenwidth = 768
......Will force the game into 1024x 768 mode
If you wish to use the default settings, change both options back to 0.