If you want neutralizing antibodies you can do serum virus neutralization assay. It's more complicated and takes longer.
Testing doesn't need to be 100% to be effective, but it does need to be better than random chance. A mixture of contact tracing, PCR testing, antibody testing and effective quarantines could be used to make the virus go away, but would require a coordinated strategy that the US has not attempted to implement, much to my dismay.
The people from the Duke-NUS Medical School have designed a "surrogate virus neutralization test"[1] which might be used to perform neutralization tests without the security requirements of using live virus.
Testing doesn't need to be 100% to be effective, but it does need to be better than random chance. A mixture of contact tracing, PCR testing, antibody testing and effective quarantines could be used to make the virus go away, but would require a coordinated strategy that the US has not attempted to implement, much to my dismay.