A challenge in the clinical adoption of cell-free DNA (cfDNA) liquid biopsies for cancer care is their high cost compared to potential reimbursement. The most common approach used in liquid biopsies to achieve high specificity detection of circulating tumor DNA (ctDNA) among a large background of normal cfDNA is to attach molecular barcodes to each DNA template, amplify it, and then sequence it many times to reach a low-error consensus. In applications where the highest possible specificity is required, error rate can be lowered further by independently detecting the sequences of both strands of the starting cfDNA. While effective in error reduction, the additional sequencing redundancy required by such barcoding methods can increase the cost of sequencing up to 100-fold over standard next-generation sequencing (NGS) of equivalent depth. We present a novel library construction and analysis method for NGS that achieves comparable performance to the best barcoding methods, but without the increase in sequencing and subsequent sequencing cost. Named Proximity-Sequencing (Pro-Seq), the method merges multiple copies of each template into a single sequencing read by physically linking the molecular copies so they seed a single sequencing cluster. Since multiple DNA copies of the same template are compared for consensus within the same cluster, sequencing accuracy is improved without the use of redundant reads. Additionally, it is possible to represent both senses of the starting duplex in a single cluster. The resulting workflow is simple, and can be completed by a single technician in a work day with minimal hands on time. Using both cfDNA and cell line DNA, we report the average per-mutation detection threshold and per-base analytical specificity to be 0.003% and >99.9997% respectively, demonstrating that Pro-Seq is among the highest performing liquid biopsy technologies in terms of both sensitivity and specificity, but with greatly reduced sequencing costs compared to existing methods of comparable accuracy.