A lawsuit filed by various citizens groups claims the machines are error-prone and easily hacked.
New Jersey election officials maintain they are secure and reliable.
Testimony started Monday in a trial that could last four weeks.
Other states have faced similar challenges to their voting systems. More than 20 states already have abandoned them.
Electronic voting opponents in New Jersey are pushing for a return to paper ballots, which could be read by laser scanners.
However, the judge made it clear yesterday that her ruling will determine the reliability of the voting machine being challenged, not recommend an alternative system.
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