Marchwood Military Port was targeted by a group called Hope and Disarmament, which suspected the base was stockpiling weapons for use against Saddam Hussein.
Two Hampshire people were among a team of self-appointed "weapons inspectors" who broke into the site by cutting a hole in the perimeter fence.
Three people were arrested, one of whom was later charged with criminal damage.
Susan van der Hijden, from Amsterdam, was given a 12-month conditional discharge at New Forest Magistrates' Court yesterday.
She later spent several hours in custody after refusing to pay the Ministry of Defence £331 compensation for damaging the fence.
Mary Gallacher, prosecuting, said van der Hijden was one of eight people who gathered outside the port at 3pm on Sunday.
She said: "The group went to Marchwood to inspect the base and get information on any weapons that were being shipped to Iraq.
"They suspected that the base was being used to supply armaments to British forces preparing to fight in the region."
Van der Hijden admitted criminal damage but said she did not deserve to be punished.
In a statement read to the court she said: "For the past ten years I have been living and working with refugees. I have seen their suffering, the scars of war and poverty on the skins and in their souls. I am lucky never to have witnessed war from close-up, but I have heard stories that have kept me awake at night.
"War is the most horrible thing that can happen to a people and yet here we are preparing for another one.
"I need to do all I can to stop the war on Iraq, even if that means breaking the law."
When van der Hijden was ordered to compensate the MoD, she replied: "I choose not to pay the compensation. I choose to go to prison."
She was held in custody until the court closed for the day.
Outside the building, fellow protester Liz Jones, of Boldre, said: "We learned a lot about what's going on at the base. Ammunition is being brought in each week. A lot of tanks were there on Monday but have now gone."
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