When you are feeling overly anxious, your heart rate might quicken, you may have sweaty palms, experience shaking or chest pain. Your blood pressure may go up. But once the situation resolves itself and the anxiety provoking moment is over, your body returns to normal. Your heart rate slows, the chest pain disappears and your blood pressure lowers.
Short-term effects on blood pressure
The rise in blood pressure from anxiety is normally short-lived. Once you are no longer anxious, your blood pressure returns to normal. According to experts, periodic rises in your blood pressure aren't necessarily dangerous and "There is no evidence that high anxiety and stress can cause long-term high blood pressure," according to Dr. Melinda Stanley, a professor in the Psychiatric and Behavioral Sciences Department at Baylor College of Medicine. 
Long-term effects on blood pressure
Periodic spikes in your blood pressure may not be dangerous but if these occur on a regular basis, it may have long lasting effects. "If you have a lot of episodes of anxiety and increased blood pressure, these can cause physical damage that is comparable to chronic high blood pressure," Stanley explains.  This can lead to heart disease, stroke, kidney damage, vision loss, and other health issues.
Additional risk factors
Research has also shown that individuals with anxiety disorders are more likely to use unhealthy habits to relieve symptoms of anxiety. These include smoking, overeating, drinking alcohol or substance abuse. These behaviors can put you at risk of high blood pressure as well. So, although anxiety may not directly cause high blood pressure, it can indirectly contribute to it.
Some medications used to treat anxiety can also cause high blood pressure. Side effects of venlafaxine (Effexor) include an increase in blood pressure and heart rate. Another class of medication monoamine oxidase inhibitors (MAOIs) (Nardil, Marplan, Eldepryl, Movergan) have a risk of causing high blood pressure when combined with certain foods, such as aged cheese, red wines, sauerkraut, dried meats and fish, chicken livers, canned figs and concentrated yeast products. If you are taking an MAOI you should speak with your doctor or pharmacist for a complete list of foods to avoid.
Because everyone reacts differently to medications, it is important to know the possible side effects and understand when you should contact a doctor.
High blood pressure is treatable
When on any type of medication, it is important to follow up with your doctor on a regular basis. If you do get a reading of high blood pressure, don't panic. Blood pressure fluctuates throughout the day, based on what you are doing, your anxiety level and even what you have eaten. Doctors normally base a high blood pressure diagnosis on several readings, done at different times on different days.
If your doctor does confirm a diagnosis of high blood pressure, he will talk to you about controlling it through diet and, if necessary, medication. He may have laboratory tests completed to be sure there is no damage to your kidneys and may want to check your glucose level, blood fats and electrolytes. Once this is done, he will be more able to recommend the best treatment for you.
See also High Blood Pressure Anxiety - How to Cope with It.
  "Control Anxiety to Stave off Spikes in Blood Pressure," 2010, May 4, Dana Benson,
"Depression: Medications," Reviewed 2012, Feb 8, Reviewed by Harvey Simon, M.D., The New York Times
"What Are the Real Risks of Antidepressants," 2005, Staff Writer, Harvard Mental Health Letter, Harvard Medical School