If you have ANY problems with UPS accepting long guns for their ground shipping or handguns for next day air please go to their website, find the address for customer service and complaints and write a short, factual and polite letter telling the corporation what the problem is. I did that about 5 years ago when our local UPS service counter gave me problems and within a few weeks their attitude changed completely.
I now ship Fedex Ground because its slightly cheaper, I can print my own labels and just drop the packages off without waiting and get an additional discount for doing that. It's a couple of miles closer to me than the UPS facility and no backtalk from the counter clerks either!
Unless you have recent model production guns you may have insurance problems. None of the companies will pay off adequately on antiques, or anything else hard to appraise. Collectibles Insurance Agency does cover shipping too, so see collectinsure.com