With some exceptions, having heart disease is not a reason to refrain from travelling. Indeed the disease itself may be the reason for travel. Simple precautions will reduce the chances of trouble.
Travel is tiring. The distances you might have to walk in airports, sometimes up and down stairs, or while sight-seeing and shopping can add up to many, many kilometres. Bags get heavier the longer you carry them. You may have difficulty in getting enough sleep, and jet lag can add to the stress of travel so careful itinerary planning is an essential part of reducing the risk. Do not be ashamed to ask for help. It can be useful to arrange for wheelchair assistance. Airlines much prefer to know in advance that you may need help rather than dealing with an emergency. Airlines also need to know if oxygen may be required as special arrangements need to be made especially on smaller aircraft.
Travelling by air is a little like exerting yourself while sitting doing nothing because of the reduced oxygen supply. Planes are pressurised to the approximate equivalent altitude of 8000 feet at which level a healthy person will be comfortable on mild exertion. If at home you are breathless at rest or with very little effort you probably are not fit to fly or will need oxygen on the trip. An airline rule of thumb is that you should be able to walk 100 metres carrying a suitcase at a reasonable pace with no discomfort. This is a minimum requirement but you should still talk to your doctor about your fitness to fly if you are on treatment for cardiac failure or if your condition is not well controlled.
Keep medications in the original pharmacy dispensed pack and have a separate list of all medication taken giving the trade and generic names as the trade names vary between countries.
Pacemakers are not affected by security screening apparatus. Because it may not be possible to access telephonic checking of pacemakers the traveller should keep details of the type and make of pacemaker, and a recent electrocardiograph tracing.