Dermatologists can â€œzapâ€ the visible veins, using an electrode needle, and make capillaries disappear. This procedure can be fairly painful, so inquire first whether the doctor uses local anesthesia. To cover broken veins with makeup, apply foundation to the area, using a concealer brush, and set with powder, using a cotton puff. If you are prone to broken capillaries, avoid extreme hot (i.e., saunas and steamrooms) and extreme cold. Excessive drinking of alcohol can lead to broken capillaries as well.