Some safety tips for senior women who travel on their own include doing thorough research on any place you plan to visit and to learn some common phrases in the local language, if it is different than your own. Another tip is to let someone else know about your itinerary and to check in with her periodically.
It is always a good idea to learn about any place you visit. Study maps, talk to others who have visited recently, and educate yourself about local culture and customs. Make sure to respect any dress codes or rules of etiquette to avoid conflict. Carry local currency, and consider purchasing a phone card in case your cell phone doesn't work.
Another good idea is to register with the U.S. Department of State before traveling abroad. If something such as a natural disaster happens in the place you're visiting, the Department of State can attempt to get in touch with you and contact a designated person back home.
Some women travelers like to carry a whistle with them in case they need to call attention to themselves quickly. It's also smart to leave expensive jewelry and watches at home. Wearing flashy things can invite theft in some places.