Do you have other info on her? I don't currently have a subscription to ancestry dot com, but I can still see some info. I got an immediate hit on a 1900 census in Ashtabula County, OH for an Emily Sweney aged 86 (birth approx 1814?)
It's tougher to find censuses under the maiden names prior to girls getting married as you may only find them on one or two prior to getting married. Emily Beckwith seems to be pretty popular, too. Don't forget to try familysearch dot org too.
Through ancesty dot com and this genforum I found out I was decended 13 generations from Matthew Beckwith of CT- the immigrant, non-royal one :)