The SARS-CoV-2 Omicron variant, with 15 mutations in Spike receptor-binding domain (Spike-RBD), renders virtually all clinical monoclonal antibodies against WT SARS-CoV-2 ineffective. We recently engineered the SARS-CoV-2 host entry receptor, ACE2, to tightly bind WT-RBD and prevent viral entry into host cells ("receptor traps"). Here we determine cryo-EM structures of our receptor traps in complex with stabilized Spike ectodomain. We develop a multi-model pipeline combining Rosetta protein modeling software and cryo-EM to allow interface energy calculations even at limited resolution and identify interface side chains that allow for high-affinity interactions between our ACE2 receptor traps and Spike-RBD. Our structural analysis provides a mechanistic rationale for the high-affinity (0.53-4.2 nM) binding of our ACE2 receptor traps to Omicron-RBD confirmed with biolayer interferometry measurements. Finally, we show that ACE2 receptor traps potently neutralize Omicron and Delta pseudotyped viruses, providing alternative therapeutic routes to combat this evolving virus.