Hundreds of loci have been associated with blood pressure (BP) traits from many genome-wide association studies. We identified an enrichment of these loci in aorta and tibial artery expression quantitative trait loci in our previous work in ~100 000 Genetic Epidemiology Research on Aging study participants. In the present study, we sought to fine-map known loci and identify novel genes by determining putative regulatory regions for these and other tissues relevant to BP. We constructed maps of putative cis-regulatory elements (CREs) using publicly available open chromatin data for the heart, aorta and tibial arteries, and multiple kidney cell types. Variants within these regions may be evaluated quantitatively for their tissue- or cell-type-specific regulatory impact using deltaSVM functional scores, as described in our previous work. We aggregate variants within these putative CREs within 50 Kb of the start or end of ‘expressed’ genes in these tissues or cell types using public expression data and use deltaSVM scores as weights in the group-wise sequence kernel association test to identify candidates. We test for association with both BP traits and expression within these tissues or cell types of interest and identify the candidates MTHFR, C10orf32, CSK, NOV, ULK4, SDCCAG8, SCAMP5, RPP25, HDGFRP3, VPS37B and PPCDC. Additionally, we examined two known QT interval genes, SCN5A and NOS1AP, in the Atherosclerosis Risk in Communities Study, as a positive control, and observed the expected heart-specific effect. Thus, our method identifies variants and genes for further functional testing using tissue- or cell-type-specific putative regulatory information.