Spectate Bots

Spectating bots as they play a new map or mod can provide invaluable feedback on a map's bot play and balance, the quality and effectivity of a mod's bot support code, or just give you an impression of how bots deal with a certain situation.

Unreal Tournament

Go to Options → Player Setup and check the Play as Spectator checkbox.
Start a botmatch as usual.

UT2003

As of build 2186 (3rd patch) you can spectate a botmatch as follows:

Go to Instant Action, select a map and a number of bots as usual and click the Spectate button.

Prior to build 2186, UT2003 doesn't provide a built-in means to spectate a botmatch; you need a third-party mutator for that.

Download the Spectate Botmatch mutator from http://mb.link-m.de/download/SpectateBotmatch.zip (8.5 kB) and install it as described in the bundled readme file.
After selecting Instant Action from the main menu and setting up your match as usual, click the Mutators tab.
Select the Spectate Botmatch mutator from the Available Mutators list to the left and click the Add button to add it to the Active Mutators list to the right.
Click the Play button to start the match.