Eritrea's climate varies dramatically with altitude. The highland plateau around Asmara sits above 2,000 meters and enjoys mild, spring-like weather for most of the year, with average temperatures around 16-20°C. The Red Sea coast around Massawa is a different world entirely -- hot and humid, regularly exceeding 40°C in summer.
October to February is the best time to visit. The highlands are dry and pleasant, the coast is at its least brutal, and the skies are clear. December through February is peak season, such as it is in a country that receives very few tourists.
March to May is still manageable in the highlands but increasingly hot on the coast. Temperatures in Massawa and the Danakil Depression can reach 50°C by May.
June to September is the rainy season in the highlands. Asmara gets most of its annual rainfall between June and August, though it typically falls in afternoon showers rather than all-day downpours. Roads outside the capital can become difficult. The coast remains dry but scorching -- this is the worst time to visit the lowlands.
If you want to visit both the highlands and the coast, aim for November to January. You will get comfortable weather in Asmara and tolerable heat in Massawa. If you are primarily interested in diving the Dahlak Islands, the calmest seas and best visibility are between October and April, with water temperatures warm year-round at around 25-28°C.
Eritrea's main public holidays are Independence Day (May 24) and Martyrs' Day (June 20). The Orthodox festivals of Timkat (January) and Meskel (September) are colorful celebrations in the highlands, worth timing a visit around if you can.