I've caught and released many 100-plus-pound tarpon on fly during every month of the year. However, as a general rule, the best times occur when the water temperature is between 72 and 88 degrees, a big push of water is present - such as around new- or full-moon phases - and little or no wind exists.
In the Florida Keys, where I now live year-round and still pursue ol' Megalops atlanticus with as much excitement as ever, these favorable conditions most often come together in April, May and June. In warmer months, the best tarpon fishing usually occurs from daylight until about 10:30 a.m. and the last couple of hours before sundown. At midday, the water temperature is usually too warm. In cooler months, try to fish a promising flat late in the afternoon when the water's had a full day to warm up.
You can encounter big tarpon in many places, but here's my list of favorite Florida areas to hunt the triple-digit specimens: Key West, Bahia Honda in the lower Keys, Islamorada in the upper Keys, and on the Gulf Coast, Boca Grande and Homosassa. All of these places offer excellent sight-fishing opportunities - the only way I fish for tarpon.
A glance at the IGFA world records on fly reveals that Florida claims all but one record - Sierra Leone being the exception - with all 100-plus-pounders caught in April or May.
You can blind-cast to rolling giant tarpon in areas such as Costa Rica's Caribbean coast, Honduras, Maracaibo (Venezuela) and deep river mouths off Gabon and Sierra Leone in Africa. Keep in mind, however, that IGFA fly rules prohibit more than 120 feet of line being used to hook a fish in order to qualify for a world-record catch. This, in effect, discourages simply letting a line sink to the bottom of a deep hole where big tarpon may be holding instead of casting to them in a traditional sight-fishing manner.