Here, we describe a novel approach for rapid discovery of a set of tumor-specific genomic structural variants (SVs), based on a combination of low coverage cancer genome sequencing using Oxford Nanopore with an SV calling and filtering pipeline. We applied the method to tumor samples of high-grade ovarian and prostate cancer patients and validated on average ten somatic SVs per patient with breakpoint-spanning PCR mini-amplicons. These SVs could be quantified in ctDNA samples of patients with metastatic prostate cancer using a digital PCR assay. The results suggest that SV dynamics correlate with and may improve existing treatment-response biomarkers such as PSA. https://github.com/UMCUGenetics/SHARC.