My father passed away and my mother was employed by him. She is now self employed and looking for health insurance. Is she eligible for COBRA benefits?

It depends on what kind of policy they had. Was it a small group plan? Or individual policies? Or part of something through a trust or association? What will probably be your best source of info is the carrier. There should be a number for customer service (maybe even on her insurance ID card) to help you better understand the kind of policy it is, and the rights that she will have. NOT all plans fall under COBRA. She may be able to convert it to an individual policy, but they are usually expensive. Make sure an individual policy covers what will be needed. (ie, NO maternity benefits, but to include prescription coverage.) If she is eligible for Medicare, make sure she gets signed up and you may want to seek a Medicare supplement policy. Good luck!