An antimicrobial coating is disclosed that provides fast transport rates of biocides for better effectiveness to deactivate SARS-CoV-2 and other viruses or bacteria on common surfaces. Some variations provide an antimicrobial structure comprising: a solid structural phase comprising a solid structural material; a continuous transport phase that is interspersed within the solid structural phase, wherein the continuous transport phase comprises a solid transport material; and an antimicrobial agent contained within the continuous transport phase, wherein the solid structural phase and the continuous transport phase are separated by an average phase-separation length from about 100 nanometers to about 500 microns. The antimicrobial structure is capable of destroying at least 99.99% of bacteria and/or viruses in 10 minutes of contact. Many options are disclosed for suitable materials to form the solid structural phase, the continuous transport phase, and the antimicrobial agent.