The James Webb Space Telescope will be able to probe the atmospheres and surface properties of hot, terrestrial planets via emission spectroscopy. We identify 18 potentially terrestrial planet candidates detected by the Transiting Exoplanet Survey Satellite (TESS) that would make ideal targets for these observations. These planet candidates cover a broad range of planet radii (R p ~ 0.6-2.0R ⊕) and orbit stars of various magnitudes (K s = 5.78-10.78, V = 8.4-15.69) and effective temperatures (T eff ~ 3000-6000 K). We use ground-based observations collected through the TESS Follow-up Observing Program (TFOP) and two vetting tools-DAVE and TRICERATOPS-to assess the reliabilities of these candidates as planets. We validate 13 planets: TOI-206 b, TOI-500 b, TOI-544 b, TOI-833 b, TOI-1075 b, TOI-1411 b, TOI-1442 b, TOI-1693 b, TOI-1860 b, TOI-2260 b, TOI-2411 b, TOI-2427 b, and TOI-2445 b. Seven of these planets (TOI-206 b, TOI-500 b, TOI-1075 b, TOI-1442 b, TOI-2260 b, TOI-2411 b, and TOI-2445 b) are ultra-short-period planets. TOI-1860 is the youngest (133 ± 26 Myr) solar twin with a known planet to date. TOI-2260 is a young (321 ± 96 Myr) G dwarf that is among the most metal-rich ([Fe/H] = 0.22 ± 0.06 dex) stars to host an ultra-short-period planet. With an estimated equilibrium temperature of ~2600 K, TOI-2260 b is also the fourth hottest known planet with R p < 2 R ⊕.