Renal denervation has a well demonstrated safety-profile. However as in any invasive test/procedure, complications can occur. The cardiologist performing the procedure, or your GP, can discuss this in more detail.
Injury to the kidney or narrowing of the renal artery are possible serious complications, though extremely rare with an incidence reported in clinical studies below 0.5%.
The most common side effect associated with renal denervation is bleeding at the entry site (groin) where the puncture is made to insert the catheter to perform the procedure. In clinical studies no major bleeding complications have been described.
The occurrence of bruising/haemathoma at the entry point though is not uncommon. This can sometimes be source of discomfort for a few days/weeks after the intervention, but it usually responds well to painkillers and tends to resolve spontaneously over time.