Many Jamaicans stocked up on food and water before the storm made itself felt on their island, but few seemed worried.
Daniel Edwards, who was bailing out his small wooden fishing boat next to a dilapidated dock in Port Royal, a small fishing village, said he wasn't overly concerned by the storm.
"It's not much of a muchness," the veteran fisherman said.
Forecasters said Ernesto could bring rain to the coast of Honduras on Monday. It is then expected to grow to near-hurricane force before moving ashore near the Belize-Mexico border early Wednesday and eventually passing into the southern Gulf of Mexico.
A tropical storm warning was issued early Monday for the coast of Honduras, from the border with Nicaragua westward to Punta Sal, including the Bay Islands. A tropical storm watch was in effect for the main island of Grand Cayman in the Cayman Islands to the north of Ernesto.
A Cayman government statement urged Grand Cayman residents to monitor the storm but said it was not likely to have serious effects on the British Caribbean territory.
Also, Mexico has issued a hurricane watch Monday for the east coast of the Yucatan Peninsula.
The U.S. hurricane center said Ernesto was centered about 145 miles east of Cabo Gracias a Dios on the Nicaragua-Honduras border early Monday. It had maximum sustained winds near 50 mph and was moving westward at 12 mph.
Far out in the Atlantic, Florence had weakened to a tropical depression Monday with maximum sustained winds near 35 mph. Additional weakening is forecast and the U.S. National Hurricane Center says Florence was expected to degenerate within the next few days.
Florence was centered about 1,610 miles east of the Northern Leeward Islands.