MIAMI — After returning from a honeymoon in the Dominican Republic, Jamie Palmeroni-Lavis asked to be tested for the Zika virus. Ms. Palmeroni-Lavis, 28, a publicist in Rochester, N.Y., wants to get pregnant, but not before she knows her body is Zika free.

But she and other would-be parents are quickly learning that getting a Zika test isn’t easy.

As worries about the spread of the virus in the United States continue to mount, public health department labs in Florida and New York City are running at or close to capacity, while private commercial labs have won emergency approval to run Zika tests and have ramped up their testing capacity.

But that doesn’t mean that just anybody can get a test. Even people like Ms. Palmeroni-Lavis, who have compelling reasons to be tested for a virus known to cause devastating brain defects in the fetus, can’t walk into a local health department and get tested on demand.

That’s because the Centers for Disease Control and Prevention has issued strict guidelines about who should be tested, giving priority to pregnant women with possible exposure to Zika and people with Zika-like symptoms. Already public health officials in Florida say they face a backlog of tests for pregnant women, some of whom may be waiting to make decisions about whether to have abortions if they test positive. But the C.D.C.’s testing policy largely ignores a sizable subgroup of women and men also at risk — those who are trying to conceive but fear they have been exposed to Zika. The C.D.C. recommends women contemplating pregnancy avoid travel to areas where Zika transmission is occurring and, if they have traveled, says they should wait at least eight weeks before trying to conceive. But it does not recommend testing.