Oh this is fun. I'm going to talk about the experience of the European explorers who came by sea during the 16th century. There were Sino-European contact through the Silk Road trade like in the travels Marco Polo, but that's not my area. (Incidently, no direct evidence of Marco Polo exist in Chinese or Mongol records.)

A few pieces of background: In the 15th century, the Portuguese crashed into the centuries-old Indian Ocean trading network that was dominated by Arab traders, and in 1511 they crowned their conquest of Indian Ocean trading ports with the capture of Malacca, the gateway into the Chinese trading world. Unfortunately for the Portuguese, China considered Malacca as part of their tributary system at the time, and they were not pleased to hear that new seaborne barbarians, who they've heard as folangji (Franks), took over the place.

The Portuguese themselves, however, were very eager to trade in China upon arriving. One captain, Simao de Andrade, even brought the slave trade into China by dealing children, even kidnapping kids off the streets. All these contributed to the very negative first impression that the Chinese have of the "Franks" at the time - in short, they were seen as cannibals, complete with a description of how the Portuguese supposedly cooked the children:

"Their method is to use a huge cauldron to heat up water until it boils, and then an iron cage with a small child in it is placed on top, and the child is steamed until sweat comes out. When the sweat is gone, [the child] is taken out, and iron scrubbers are used to scrape away the bitter flesh. The child is still living at this point. Then they kill it, excise the stomach, take out the intestines, and steam and eat it."

Soon the Portuguese made themselves so unwelcome the Chinese assembled a fleet and chased them away. Although the Chinese were successful, they came to appreciate the superiority of European guns and cannons, which were copied and spread across the land - the cannons in particular were placed along the Great Wall. They were so impressed by the new firearms that they wrote laudatory poems to celebrate their power! Here is one, translated, that describes what happens if you shoot it for seven times:

The first boom rouses the courage of the soldiers

The second boom flays the skin of the evil officials

The third boom and raging flames roast the red cliffs

With the fourth sky-shaking boom come the capital troops

The fifth boom: a torrent, and the lakewaters stand up

The sixth boom and the seventh boom - the wind roars

Thunder cracks, the waves are everywhere, an iron hammer rings.

Meanwhile, the Portuguese were prevented from trading in China in an official capacity. They left the Cantonese waters where they were defeated and continued their trade near the city of Ningbo where they collaborated with Chinese smugglers to continue their trade. These smugglers were led by the pirate lord Wang Zhi, whose confederation of pirates spread from the Japanese island of Kyushu to the ports of Malaysia and Indonesia in the south. In 1542, a pirate junk carrying Wang Zhi and three Portuguese adventurers were on its way from Thailand to Ningbo, but they sailed into a storm and ended up on the small Japanese island of Tanegashima. This was the first time Europeans came to Japan, and we have a relatively good idea what went down.

The Japanese and the Portuguese had no idea how to communicate with each other. Fortunately, Wang Zhi, despite not knowing how to speak Japanese, was able to communicate with the Japanese by writing Chinese in the sand, since Chinese and Japanese shared the same script at the time - then apparently Wang translated the Japanese to Portuguese (we don't know whether he himself was fluent in Portuguese or someone in his crew was). Describing the Portuguese to the Japanese, Wang Zhi said:

"These men are traders of the Southwest Barbary (Sei Nanban). They understand to a certain degree the distinction between Superior and Inferior, but I do not know whether they have a proper system of ceremonial etiquette. They eat with their fingers instead of with chopsticks such as we use. They show their feelings without any self-control. They cannot understand the meaning of written characters. They are people who spend their lives roving hither and yon. They have no fixed abode and barter things which they have for those they do not, but withal they are a harmless sort of people."

These are, of course, the impression of a Chinese man who has only seen the Portuguese as sailors, traders, and sometimes haughty fidalgo (noblemen). The Portuguese's eating with their hands seemed to be something deserving of special derision, since the travel writer Pinto wrote that even a serving maid made fun of them for not using the chopsticks when attending a banquet in Kyushu.

Back to the meeting on Tanegashima, the most important thing that happened here was the transfer of the gun to the Japanese. The Japanese were like the Chinese for their reaction to the gun. In a record about a Portuguese demonstration of the gun on Tanegashima, it was said that: "People were at first startled, then they became frightened. In the end, however, they all said in unison: ‘We would like to learn!’" Then the technology was spread throughout the warring lands and one warlord Oda Nobunaga used it to great effect, starting the reunification of Japan.

That's all for now, I think! See also this post for some more Chinese reactions towards European military technology and sciences!

Sources:

• C. R. Boxer, The Christian Century of Japan
• Tonio Andrade, The Gunpowder Age
• Olof G. Lidin, Tanegashima