Porcine viruses have been emerging in recent decades, threatening animal and human health, as well as economic stability for pig farmers worldwide. Next-generation sequencing (NGS) can detect and characterize known and unknown viruses but has limited sensitivity when an unbiased approach, such as shotgun metagenomics sequencing, is used. To increase the sensitivity of NGS for the detection of viruses, we applied and evaluated a broad viral targeted sequence capture (TSC) panel and compared it to an unbiased shotgun metagenomic approach. A cohort of 36 pooled porcine nasal swab and blood serum samples collected from both sides of the Dutch–German border region were evaluated. Overall, we detected 46 different viral species using TSC, compared to 40 viral species with a shotgun metagenomics approach. Furthermore, we performed phylogenetic analysis on recovered influenza A virus (FLUAV) genomes from Germany and revealed a close similarity to a zoonotic influenza strain previously detected in the Netherlands. Although TSC introduced coverage bias within the detected viruses, it improved sensitivity, genome sequence depth and contig length. In-depth characterization of the swine virome, coupled with developing new enrichment techniques, can play a crucial role in the surveillance of circulating porcine viruses and emerging zoonotic pathogens.