Yes, and even their newspapers kept correspondents in the city.

Max Schnetzer of the Swiss newspaper Der Bund, stayed in Berlin until the end, writing from a post near the Brandenburg Gate. He counted the Soviet shells as they came in:

"... in the center of the government section of the Wilhelmstrasse at least one shell was landing every five seconds. Then there would be a pause of half a minute or a minute and once again the shells would start to fall. From where he stood the newspaperman could see fires shooting up toward the skies from the direction of the Friedrichstrasse Station. 'Because the smoke and haze diffuses the light, it looks as if the very clouds are on fire.'"

That's from Ryan's The Last Battle.

David Paul's The Last Days of the Swiss Embassy in Berlin was published in 1948, and he was able to talk to many of the people who worked at the embassy.

In Japan, Swiss minister Camille Gorge and Portuguese minister Fernandes stayed at their posts, reporting on the happenings in that country.

Why did they stay? G.R. Berridge's Embassies in Armed Conflict takes a stab at this. On page 87 of that book, he quotes a U.S. State Department telegram to Brussels in August 1914, at the start of World War I:

"In this critical hour it becomes necessary for our Government to render every assistance that a neutral can render, not only as an international duty, but that we may be in a better position to exert our influence for peace."

First of all - during ww2, only the grand powers maintained embassies headed by an ambassador to each other. All other nations had a lower level of diplomatic representation, often a legation headed by a minister.

The Swedish legation in Berlin consisted of 1 minister, 4 military attachés and 8 other staff. The priest in residence in the Victoria parish, the Swedish lutheran church in Germany was also closely tied to the embassy (three priests manned this position during the war and all three made efforts to aid Jewish refugees).

A bunker was built on the legation grounds in summer 1943, which was used when the legation buildinds were destroyed in a fire as a result of allied bombings on the 22nd of November 1943. Most of the legation moved to the castle Alt Döbern 120km southwest of Berlin after the fire, but some activity remained in the bunker. During Spring 1945, the legation moved to the castle Friedrichsruh outside Hamburg.

The legation bunker was reached by Soviet Soldiers on the 1st of May. As far as I can find, the Soviets respected the diplomatic status of the Swedish personell in the bunker.

On the 18th of May 1945, the entire legation was with Soviet and Western Allied approval, withdrawn to Sweden.

My knowledge on this subject is limited, but Cesare Orsenigo was the nuncio to Germany, which made him the rough equivalent of the Vatican's ambassador in that country. The Vatican was neutral during WWII, which was a treaty requirement of the 1929 Lateran Accords. My information on Orsenigo comes via studying his predecessor in that position, Eugenio Pacelli. Pacelli became Pope Pius XII in 1939, and Orsenigo had been nuncio to Germany for nine years at that time. I do not have information regarding all of his movements during the war, but he only left Berlin in February of 1945 (and took up residence in Bavaria). Orsenigo was (and is) a controversial figure, as he is viewed as being overly accommodating to the Nazi regime and insufficiently active in his protests of Nazi actions. He was also effectively sidelined by Pius XII's policy of handling relations with Germany personally, which left Orsenigo with little to do on the diplomatic front.

I don't have any real information on the Vatican's envoy to Japan (apostolic delegate Paolo Marella), and I have little information on his travels. My studies of Pius XII have focused much more on the European theater rather than the Pacific.