Simarteriviruses (Arteriviridae: Simarterivirinae) are commonly found at high titers in the blood of African monkeys but do not cause overt disease in these hosts. In contrast, simarteriviruses cause severe disease in Asian macaques upon accidental or experimental transmission. Here, we sought to better understand the host-dependent drivers of simarterivirus pathogenesis by infecting olive baboons (n = 4) and rhesus monkeys (n = 4) with the simarterivirus Southwest baboon virus 1 (SWBV-1). Surprisingly, none of the animals in our study showed signs of disease following SWBV-1 inoculation. Three animals (two rhesus monkeys and one olive baboon) became infected and sustained high levels of SWBV-1 viremia for the duration of the study. The course of SWBV-1 infection was highly predictable: plasma viremia peaked between 1 × 107 and 1 × 108 vRNA copies/mL at 3–10 days post-inoculation, which was followed by a relative nadir and then establishment of a stable set-point between 1 × 106 and 1 × 107 vRNA copies/mL for the remainder of the study (56 days). We characterized cellular and antibody responses to SWBV-1 infection in these animals, demonstrating that macaques and baboons mount similar responses to SWBV-1 infection, yet these responses are ineffective at clearing SWBV-1 infection. SWBV-1 sequencing revealed the accumulation of non-synonymous mutations in a region of the genome that corresponds to an immunodominant epitope in the simarterivirus major envelope glycoprotein GP5, which likely contribute to viral persistence by enabling escape from host antibodies.