Stillbirth Awareness and Research Act of 2013 - Amends the Public Health Service Act to direct the Secretary of Health and Human Services (HHS), acting through the Director of the Centers for Disease Control and Prevention (CDC), to establish and maintain a scientific registry of stillbirths in the United States, which shall include for each stillbirth information on the stillborn fetus and the mother's health and pregnancy as collected and submitted by states on the U.S. Standard Report of Fetal Death.

Requires the Secretary to: (1) provide for the development of a standard definition of stillbirth and a standard protocol for stillbirth data collection and surveillance, and (2) carry out a national campaign to increase public and state awareness of such definition and protocol and public awareness and knowledge of stillbirths.

Expresses the sense of Congress that the Director of the National Institutes of Health (NIH) should increase the allocation of funds and other resources for stillbirth research.