Genome engineering is a powerful tool for in vitro research and the creation of novel model organisms and has growing clinical applications. Randomly integrating vectors, such as lentivirus- or transposase-based methods, are simple and easy to use but carry risks arising from insertional mutagenesis. Here we present enhanced-specificity tagmentation-assisted PCR (esTag-PCR), a rapid and accurate method for mapping transgene integration and copy number. Using stably transfected HepG2 cells, we demonstrate that esTag-PCR has higher integration site detection accuracy and efficiency than alternative tagmentation-based methods. Next, we performed esTag-PCR on rhesus macaque embryos derived from zygotes injected with piggyBac transposase and transposon/transgene plasmid. Using low-input trophectoderm biopsies, we demonstrate that esTag-PCR accurately maps integration events while preserving blastocyst viability. We used these high-resolution data to evaluate the performance of piggyBac-mediated editing of rhesus macaque embryos, demonstrating that increased concentration of transposon/transgene plasmid can increase the fraction of embryos with stable integration; however, the number of integrations per embryo also increases, which may be problematic for some applications. Collectively, esTag-PCR represents an important improvement to the detection of transgene integration, provides a method to validate and screen edited embryos before implantation, and represents an important advance in the creation of transgenic animal models.