Droplet microfluidic platforms have greatly enhanced the throughput and sensitivity of single-molecule and single-cell analyses. However, real-time analyses of individual droplets remain challenging. Most droplet microfluidic platforms have fundamental drawbacks that undermine their utility toward applications that rely on real-time monitoring to identify rare variants, such as bacterial persistence, drug discovery, antibody production, epigenetic biomarker analyses, etc. We present a platform for high-density droplet trapping and real-time analysis with 100% loading and trapping efficiency at a packing density of 110,000 droplets per in2. To demonstrate real-time analysis capabilities, we perform digital PCR and parallelized digital high-resolution melt curve acquisition on droplets to discriminate methylation levels of a tumor suppressor gene, CDO1, on a molecule-by-molecule basis. We hope that this platform, which is compatible with a large range of droplet sizes and generation technologies, may facilitate high-throughput real-time analyses on a molecule-by-molecule or cell-by-cell basis of heterogeneous populations.