Foods to avoid: - Salt or sodium - Deli meat - Frozen pizza - Pickles - Canned soups - Canned tomato products - Sugar - Processed foods with trans or saturated fat. What's the best drink for high blood pressure? Some drinks can help lower your blood pressure, including: skimmed milk. Low-fat dairy products like yogurt and skimmed milk can help lower high blood pressure. Tomato juice. Beet juice. Hibiscus tea. Pomegranate juice.