Many patients are concerned about traveling to high altitudes, such as Denver Colorado (the mile high city). Practically, flying from Chicago to Denver is rarely a source of major problems, but if one then goes on to 10000 feet, there may be more issues.
Altitude is categorized as low, moderate, high, very high, and extreme. "High" altitude begins at 2400 meters -- i.e. Denver would qualify, "Very high" at 4000 meters, and extreme at 5,500 meters. Pikes Peak in Colorado is about 4000 meters, and thus "Very high". Mt. Everest, at 9000 meters, is beyond "extreme".
Here were are discussing acute mountain sickness (AMS)-- the least severe of the subtypes of altitude sickness. According to Santantonio et al, about half of all travelers to high altitudes report AMS. Others report less, but nevertheless still a considerable number (MacInnis et al, 2013). A headache is required for the diagnosis of AMS (Alizadeh et al, 2012). Additionally there may be fatigue, weakness, nausea, vomiting and anorexia (no appetite). In other words, pretty similar to a bad migraine.
Risks for altitude sickness include rapid rate of ascent, although not all reports agree (Hsu et al, 2015). It can often be prevented by slowing ascent above 2500 meters, to no more than 500 meters/day. The best treatment for altitude sickness is immediate descent by at least 1000 meters. Those who already live at moderately high altitudes are more resistant to AMS (Staab et al, 2013).
Medications for altitude sickness include acetazolamide twice/day (DeLillis et al, 2013), or dexamethasone (Carod-Artal, 2014). The rationale for both appear to be mainly related to prevention of cerebral edema. Some authors suggest that the mechanism for action is actually migraine prophylaxis (Kim and Kim, 2011). We find this dubious.
The mildest form of altitude sickness, AMS, includes symptoms that overlap substantially with migraine including headache, nausea, vomiting and lack of appetite. The most reliable method of avoiding it is likely acclimatization -- avoid rapid ascent once one is above 2500 meters. In other words, if you travel to Colorado, it might be best to defer your trip up Pikes Peak for a few days.