My knowledge of what goes on in the Muggle world is that one calls the coroner up on the phone, or if they're not sure what to do, dialing 911 (or the equivalent) is acceptable, at all hours, and I assume there must be wizard coroners. But wizards don't have phones, and not everyone has owls, and even if they did, that seems to be an awfully inefficient method to deliver the message, "Please take my dead husband's body away." There's the method of using one's Patronus, but that seems to be an Order-of-the-Phoenix-only thing. I feel like I must be missing something obvious.
EDIT: Thank you everybody, you've all been a great help (and also have made me feel better about how I handled my own mother's passing, because I was sure in retrospect dialing 911 was the long way to do it). I had completely forgotten about Floo Powder. Contacting the Aurors also neatly takes care of another plot point I'd been semi-fudging anyway, so, hooray!