More importantly here in New Hampshire, and you didn't ask, is Administrative License Suspension. You more than likely got a pink slip of paper explaining ALS. Many people come to me after stashing the crinkly thin paper away, not reading the fine print that automatically "administratively" takes your license away in 30 days. You have the right to ask for an ALS hearing and hold the officers to their procedural duties, as explained on the back of that form.
Directly answering your question, the only way to really "prove" the negative that you were not drunk would be to hire a toxicologist. If you had an actual blood test at some point after the stop, a toxicologist could draw a time line, calculating what your blood alcohol level would have been at the time the officer stopped you.
Toxicologists use inverse interpolation, a physiological calculation based on body metabolism, weight, age and other factors. The problem here is that the toxicologists I've hired for litigation cost in the range of $3,000 to $5,000.
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Andrew Myers of Derry has law offices in Derry and North Andover. He is a member of the American Association for Justice and the New Hampshire Trial Lawyers Association. Send questions to email@example.com.