Conception certificates are not issued in the United States. There is no legal basis to identify a fetus as a viable human being until such time as that fetus has survived extrication from the womb and begun to respire on it's own--a condition technically referred to as 'birth'.
Prior to 'birth' a number of calamities may befall the fetus--and/or mother--that ultimately prevent 'birth' from taking place. Even with the vast advances made in perinatal care in the last half century or so, there are a great many tragic outcomes each year to sucessful ova fertilization and uterine implantation--the condition commonly referred to as 'conception'.
Although the Infant Mortality Rate in the US is among the lowest in the world--and our perinatal care providers are the world's best--there are still many, many cases of women whose pregnancies are terminated prematurely as a result of trauma or natural biological processes.
Birth Certificate. One is required in order to have a Death Certificate. Aborted fetuses are not issued death certificates. Any parturition prior to full term that results in a non-viable issue does not receive the designation of a living, breathing person.
Although emotions run high whenever a pregnant woman is injured or killed, there must be a line, a definition, a starting point for life that is codified by law. This ensures fairness in the face of emotion and will prevent the "moving the goalposts" phenomenon that seems to plague attempts at rational legislation in this area.