The drones have crashed into the chimney of a power plant in Estonia, hit empty fuel tanks in Latvia and been shot down by Romanian fighter jets stationed in Lithuania.
Ukrainian officials apologised, saying the drones had been aimed at military targets inside Russia but were sent off course by Russian electronic interference.
Estonia is hosting the summit in its capital, Tallinn.
The country holds the rotating presidency of the NB8, a regional grouping of the five Nordic countries and the three Baltic states.
It brought together the bloc's prime ministers, along with Zelenskiy.
Zelenskiy and Estonian President Alar Karis agreed to work on cheaper ways to shoot down drones that have flown over Estonia, including one that a NATO fighter jet shot down over the south of the country in May.
"We have shown that we can shoot the drones down with the planes," Karis said on Tuesday during a joint news conference in Tallinn.
But using fighter jets to shoot down the drones is very expensive, Karis said, so he hopes to partner with Ukraine for its technology and expertise to do so more cheaply.
Zelenskiy said Ukraine was ready to do so, drawing on experience it had built up helping countries in the Middle East shoot down drones, where it had sent expert teams to train local forces.
"We did this in the Middle East, and it worked," he said.
He said Ukraine could offer the low-cost interceptor drones it has deployed at home to build an inexpensive shield against Russian drone attacks, and that Kyiv could send expert teams to its European partners "at any moment".
Karis said he expected drones to cross into Baltic airspace as the war continued and urged the public to remain calm.
Estonia and the other Baltic states are among Ukraine's staunchest supporters in its war against Russia.
The Estonian leader said the Baltic country supported Ukraine's bids to join the EU and NATO.
He also called for stronger sanctions on Russia.
Meanwhile, Russia kept up its strikes across Ukraine.
In the northeastern Kharkiv region, three people were killed and 25 others, including three children, were wounded in attacks in the past 24 hours, said Oleh Syniehubov, head of the regional administration.
In the Dnipropetrovsk region, three people were wounded when several districts came under attack overnight, said regional administration head Oleksandr Hanzha.
Russia launched 166 long-range strike drones and two guided missiles at Ukraine overnight, the Ukrainian air force said.
Air defences shot down 146 of the drones, it said.
Russia's defence ministry said air defences downed 140 Ukrainian drones overnight.
A woman was killed when a Ukrainian drone hit an apartment building in the Belgorod region, regional emergency officials said.
Ukrainian Foreign Minister Andrii Sybiha also travelled to Tallinn, where he met his Estonian counterpart, Margus Tsahkna.
The two discussed Ukraine's security, pressure on Russia, and Kyiv's bid to join the European Union, Tsahkna said.
"Estonia will continue to stand by Ukraine for as long as it takes," Tsahkna wrote on X.
As Russian President Vladimir Putin "intensifies his attacks and shows no sign of abandoning his imperial ambitions, our responsibility is to increase pressure, not offer concessions".
Separately, Zelenskiy said on Monday that he had held positive talks with US representatives Steve Witkoff and Jared Kushner during a stopover at an airport in Moldova's capital, describing them as focused on ending the war.
