UPDATE: Yes, we still have Quarantine Stations, operated by the CDC:
U.S. Quarantine Stations are located at 20 ports of entry and land-border crossings where international travelers arrive. They are staffed with quarantine medical and public health officers from CDC. These health officers decide whether ill persons can enter the United States and what measures should be taken to prevent the spread of infectious diseases.You might be interested in this advice to airlines:
Quarantine officers are responsible for activities as various as responding to reports of illnesses, to screening cargo and inspecting animals and animal products, to monitoring the health of and collecting any medical information of new immigrants, refugees, asylees, and parolees.
Updated October 15, 2014
CDC requests airline crews to ask sick travelers if they were in Guinea, Liberia, or Sierra Leone in the last 21 days.
If YES, AND they have any of these Ebola symptoms—fever, severe headache, muscle pain, vomiting, diarrhea, stomach pain, or unexplained bruising or bleeding—report immediately to CDC.
If NO, follow routine procedures.