If you don't locate what you're looking for trying Insweb, use another internet service such as esurance.  Esurance not only provides a comparison of New Hampshire automobile insurance rates, but it also has a wealth of information about buying car insurance.  If you still aren't satisfied, the next step is to pick up the telephone and call major insurance companies.  Most states such as New Hampshire have representatives from the big insurance companies, like State Farm and Allstate.  You can also try national companies like Geico.