Methods and kits for delivering pharmaceutical agents to an adventitia and other regions outside an external elastic lamina (EEL) surrounding a blood vessel utilize a catheter having a needle. The needle is positioned in up to 5 mm beyond the EEL and delivers an amount of a pharmaceutical agent sufficient to circumferentially permeate around the blood vessel and, in many cases, extend longitudinally and radially along the blood vessel. Confirmation that a delivery aperture of the needle lies beyond the EEL may be required before delivering the pharmaceutical agent. In one example, catheters are used to deliver dexamethasone and other anti-inflammatory agents to a peripheral vasculature and other vasculature to treat peripheral vascular disease and other conditions.