Mosquito-borne dengue (DENV) and Zika (ZIKV) viruses originated in Old World sylvatic cycles involving monkey hosts, spilled over into human transmission, and were translocated to the Americas, creating potential for spillback into neotropical sylvatic cycles. Studies of the trade-offs that shape within-host dynamics and transmission of these viruses are lacking, hampering efforts to predict spillover and spillback. We exposed native (cynomolgus macaque) or novel (squirrel monkey) hosts to mosquitoes infected with either sylvatic DENV or ZIKV and monitored viremia, natural killer cells, transmission to mosquitoes, cytokines, and neutralizing antibody titers. Unexpectedly, DENV transmission from both host species occurred only when serum viremia was undetectable or near the limit of detection. ZIKV replicated in squirrel monkeys to much higher titers than DENV and was transmitted more efficiently but stimulated lower neutralizing antibody titers. Increasing ZIKV viremia led to greater instantaneous transmission and shorter duration of infection, consistent with a replication-clearance trade-off.