The deficiency of natural anticoagulants—antithrombin (AT), protein C (PC), and protein S (PS)—is a highly predisposing factor for thrombosis, which is still underdiagnosed at the genetic level. We aimed to establish and evaluate an optimal diagnostic approach based on a high-throughput sequencing platform suitable for testing a small number of genes. A fast, flexible, and efficient method involving automated amplicon library preparation and target sequencing on the Ion Torrent platform was optimized. The cohort consisted of a group of 31 unrelated patients selected for sequencing due to repeatedly low levels of one of the anticoagulant proteins (11 AT-deficient, 13 PC-deficient, and 7 PS-deficient patients). The overall mutation detection rate was 67.7%, highest in PC deficiency (76.9%), and six variants were newly detected—SERPINC1 c.398A > T (p.Gln133Leu), PROC c.450C > A (p.Tyr150Ter), c.715G > C (p.Gly239Arg) and c.866C > G (p.Pro289Arg), and PROS1 c.1468delA (p.Ile490fs) and c.1931T > A (p.Ile644Asn). Our data are consistent with those of previous studies, which mostly used time-consuming Sanger sequencing for genotyping, and the indication criteria for molecular genetic testing were adapted to this process in the past. Our promising results allow for a wider application of the described methodology in clinical practice, which will enable a suitable expansion of the group of indicated patients to include individuals with severe clinical findings of thrombosis at a young age. Moreover, this approach is flexible and applicable to other oligogenic panels.