Nir Liberboim, founder of Uprise Ventures, wondered how the start-up planned to convert its subscribers into customers who also purchase full bottles after their monthly tastings.
"Creating a memorable experience is really the best way to add value and create that brand loyalty," said Vodofsky.
Alicia Syrett, a board member of the New York Angels, questioned how the start-up would retain users after they "discovered their taste."
Dukes said they've tailored the program so that, "You can make indications on what you liked [and] what you didn't like through your online account. Then we can cater more towards your taste."
The San Francisco-based start-up is reportedly self-funded, and has two employees.
Vinebox is accepting pre-orders, and its first boxes will begin shipping in January 2016.
Dukes said members can expect wines from Chateau Maison Blanche in Saint-Emilion, France, and oak-aged Chardonnay from Domaine du Chardonnay of Chablis in their first orders.
"We have ambitious plans for the future," Dukes told CNBC, "including additional membership options, enhanced recommendation algorithms, and several retail and growth opportunities."