“I got the test done and was able to go on with my life,” said Ms. Herndon, who lives in Fort Polk, La.

Estimates of the extent of paternal uncertainty vary.

Studies have found a discrepancy rate — when the presumed father is not the biological father — of anywhere from 0.8 percent to 30 percent, with the median being 3.7 percent, according to one review of such studies. Another study found that about 9 percent of birth certificates in Florida, even excluding births to teenage mothers, did not list the full names of the father, though it was not clear how much of this was related to uncertainty. Infant mortality was higher in those cases than if the father’s name was on the birth certificate.

It has already been possible to determine paternity during pregnancy using amniocentesis or chorionic villus sampling, the same medical procedures used to test a fetus for Down syndrome. But those procedures are invasive and carry a small risk of inducing a miscarriage, so they are rarely used for paternity testing.

By contrast, the new tests require only blood samples from the pregnant woman and the potential father. And doctors generally do not have to be involved.

That could vastly expand testing, said Sara Katsanis of Duke University’s Institute for Genome Sciences and Policy. She is planning a study with one of the testing companies to see if prenatal paternity testing can reduce a pregnant woman’s stress.

Some noninvasive paternity tests have been offered over the Internet for about a decade, and there have been various complaints about inaccurate or even fraudulent results.