The most prominent of the IRAS debris disk systems, α Lyrae (Vega), at a distance of 7.7 pc, has been observed by both the NIRCam and MIRI instruments on the James Webb Space Telescope. This paper describes NIRCam coronagraphic observations, which have achieved F444W contrast levels of 3 × 10−7 at 1″ (7.7 au), 1 × 10−7 at 2″ (15 au), and a few × 10−8 beyond 5″ (38 au), corresponding to masses of <3, 2, and 0.5 M
J for a system age of 700 Myr. Two F444W objects are identified in the outer MIRI debris disk, around 48 au. One of these is detected by MIRI and appears to be extended with a spectral energy distribution similar to those of distant extragalactic sources. The second one also appears extended in the NIRCam data suggestive of an extragalactic nature. The NIRCam limits within the inner disk (1″–10″) correspond to model-dependent masses of 2–3 M
J. K. Y. L. Su et al. argue that planets larger than 0.3 M
J would disrupt the smooth disk structure seen at MIRI wavelengths. Eight additional objects are found within 60″ of Vega, but none have astrometric properties or colors consistent with planet candidates. These observations reach a level consistent with expected Jeans mass limits. Deeper observations achieving contrast levels < 10−8 outside of ∼4″ and reaching masses below that of Saturn are possible, but may not reveal a large population of new objects.