The contraceptive pill and HRT (or hormone replacement therapy) both contain the hormone estrogen which may have an affect on your blood pressure.
Almost every woman who takes the pill experiences a slight rise in blood pressure and usually that is not too much of a problem. About 5% of women experience a more marked rise in blood pressure and if that is combined with other risk factors (such as a previous problem with high blood pressure, smoking, being over 35 or overweight) she might very well be advised by her doctor to stop taking it or to replace it with a low-estrogen or progesterone-only pill.
Normally blood pressure is monitored more regularly for women on the pill to catch any problems, but you should always contact your doctor immediately if you experience any worrying side effects. (For a list of symptoms to watch out for read the up-to-date instructions which comes with your particular pill).
Fortunately if blood pressure does rise, it is generally not a long term problem (at least as far as the pill is concerned). Once the pill is stopped it ceases to have an affect on blood pressure within a few weeks.
HRT (or hormone replacement therapy) is prescribed to help with the symptoms of the menopause which are caused by a reduction in estrogen production. Although it contains estrogen, HRT generally has less of the hormone than the contraceptive pill and therefore does not tend to affect blood pressure so much.
As long as blood pressure is checked regularly HRT has been found to be quite safe for most women as far as high blood pressure is concerned and your doctor will make sure that it is safe for you before prescribing it.