Tests for COVID-19 generally measure SARS-CoV-2 viral RNA from nasal swabs or antibodies against the virus from blood. It has been shown, however, that both viral particles and antibodies against those particles are present in saliva, which is more accessible than both swabs and blood. We present methods for highly sensitive measurements of both viral RNA and antibodies from the same saliva sample. We developed an efficient saliva RNA extraction method and combined it with an ultrasensitive antibody test based on single molecule array (Simoa) technology. We apply our test to the saliva of patients who presented to the hospital with COVID-19 symptoms, some of whom tested positive with a conventional RT-qPCR nasopharyngeal swab test. We demonstrate that combining viral RNA detection by RT-qPCR with antibody detection by Simoa identifies more patients as infected than either method alone. Our results demonstrate the utility of combining viral RNA and antibody testing from saliva, a single easily accessible biofluid.