Recent advancements in long-read sequencing have enabled the telomere-to-telomere (T2T) assembly of a human genome and are now contributing to the haplotype-resolved T2T assemblies of multiple human genomes. Since the accuracy of read mapping tools deteriorates in highly-repetitive regions, there is a need to develop accurate, error-exposing (detecting potential assembly errors), and diploid-aware (distinguishing different haplotypes) tools for read mapping in T2T assemblies. Although TandemMapper and Winnowmap2 tools made the first steps toward this goal, they have limitations. We describe the first accurate, error-exposing, and (to a limited extent) diploid-aware VerityMap tool for long-read mapping to T2T assemblies. Github: https://github.com/ablab/VerityMap