The simple answer is yes they can increase your risk of having a cardiovascular event.
By event I am talking about increased risk of clot formation which can lead to heart attacks and stroke.
The earlier contraceptives used higher levels of estrogen than the newer formulations. The newer formulations use lower doses of estrogen, which is safer in terms of lowering the risk of blood clots, and they tend to use a progestin, a synthetic version of progesterone that is not likely to raise blood pressure and may even slightly reduce it.
Since 2000, death rates have increased in women between the ages of 35 and 44, while all other age groups have seen a decline. Among factors that may be contributing to the rise are increases in obesity and smoking, a decline in physical activity at this time in life, and a significant increase in the use of oral contraceptives.
Women at high risk for cardiovascular problems, especially those who smoke, should consider alternative forms of contraception.