I assume you are sure that your monitor has a higher resolution.

In my xorg.conf file this is what I have:

Section "Monitor"
Identifier "Envision EFT920"
Option "DPMS"
HorizSync 30-100
VertRefresh 50-160
EndSection

Section "Screen"
Identifier "Default Screen"
Device "Intel Corporation 82845G/GL [Brookdale-G]/GE Chipset
Integrated Graphics Device"
Monitor "Envision EFT920"
DefaultDepth 24
SubSection "Display"
Depth 1
Modes "1600x1200" "1280x1024" "1280x960" "1024x768" "800x600" "640x480"
EndSubSection
SubSection "Display"
Depth 4
Modes "1600x1200" "1280x1024" "1280x960" "1024x768" "800x600" "640x480"
EndSubSection
SubSection "Display"
Depth 8
Modes "1600x1200" "1280x1024" "1280x960" "1024x768" "800x600" "640x480"
EndSubSection
SubSection "Display"
Depth 15
Modes "1600x1200" "1280x1024" "1280x960" "1024x768" "800x600" "640x480"
EndSubSection
SubSection "Display"
Depth 16
Modes "1600x1200" "1280x1024" "1280x960" "1024x768" "800x600" "640x480"
EndSubSection
SubSection "Display"
Depth 24
Modes "1600x1200" "1280x1024" "1280x960" "1024x768" "800x600" "640x480"
EndSubSection
EndSection

If you dont have something similar, you can write it. Go do your monitor
manufacturer site and get the specs.

Xorg.conf is one way.

Easier to first go to [depending how your set up] a menu editor and
Other then look for "Screens and Graphics" check the box so it is
available in the menu.

Go to:
Applications--Other--Screens and graphics [select your monitor and
resolution]. I have a Samsung monitor on my spare machine and i always
use this method. Ubuntu seem to do one or two odd things from version
to version. The location of the "Screens and Graphics" for one thing -
some hardware seems to get left out in later versions and yet was in
say 7.04.

I tried this using 8.1. Screen Resolution is in the
"System-Preference" area. I couldn't find anything that had to do with
selecting a monitor. Couldn't find anything like "Screens and
Graphics" either. Displayed resolution included 1680x1050 which is
what I am using, but I wanted to try your solution.

Changed it to 1400x1050. It changed ok, but looked awful. Tried to
change back to 1680x1050, and it wouldn't change. Had to restart. It
came back as original - 1680x1050.

I did say go to Menu editor and add the Screens & Graphics bar. Like
the Floppy formatter it is not there by default [i don't know why it
was in earlier versions]. Then you will find it. All in previous post.

I clicked on "Edit Menus". That took me to "Main Menu" which is also
accessible under System-Preferences. "Screen Resolution" is
available, checked and usable in Preferences. That option, when run
provides the button "Detect Displays" which detects nothing as far as
I can tell. I'm using a Samsung which is plug and play. I checked
all the available menu items - some checked, some not. Can't find
anything that looks like "Screens & Graphics".

If I click on "New Item" or "New Menu" in the Menu Editor it wants to
know commands and locations. I know neither.