Federated States of Micronesia (FSM)



Even though Micronesia is a federation, all member states (Pohnpei, Chuuk, Yap, Kosrae) are sovereign regarding immigration. Hence, passports get checked and stamped even when flying from one state to the next. And all passengers have to pay a departure fee to the state.
Fiji



On my travels through the South Seas, I got many Fijian passport stamps: Fiji is a hub for flights to smaller island nations in Melanesia and Polynesia. Fiji has two international airports, whose codes are visible as part of the number below the date on the stamps: Nadi (NAN) and Nausori (NSI). There are even domestic flights from Nadi to Nausori.
Kiribati


Kiribati has two international airports: Bonriki on Tarawa Atoll in the Gilbert Islands, and Cassidy on Kiritimati Island in the Line Islands. The distance between these airports is 3.288 km, and there are no direct flights linking them. Instead a rather long detour via Fiji is required.
Marshall Islands



The Republic of the Marshall Islands is a cool country for passport stamp collectors: One of its atolls, Kwajalein, serves as an U.S. army base. On its airport, Bucholz Army Airfield, both the Marshall Islands and the U.S. army do immigration checks – and you get a passport stamp of both! Due to the military character of this atoll, travelling there is not easy, but possible – read more here.
Nauru



Getting a visa for Nauru is a challenge. According to official information, an x-ray of the chest and a police certificate record are required. Much more difficult was, as it turned out, getting a hotel confirmation and doing a payment to an obscure little Australian bank. Read here all the details. But it was absolutely worth it: Nauru is clearly the most unconventional und surprising destination in Oceania.
Northern Marianas (CNMI)

Sadly, the Northern Marianas lost control over immigration to the United States in 2009. Sadly for me, because when entering the Northern Marianas from the US territory of Guam, I got no passport stamp. Sadly for the Marianas, because they cannot decide anymore on whom to issue a visa. Here is the stamp I got on my boarding pass when leaving the Commonwealth again.
Palau


Back in 2017, Palau had the most beautiful passport stamps all over Oceania (with the exception of the Cook Islands, possibly), featuring the shape of a sea shell and a Bai, the traditional assembly hall of village councils. Only four Bai have been preserved. Shortly after my visit, a new passport stamp was introduced: It’s called «Palau Pledge» and covers an entire passport page. It includes a poem, by which the visitor pledges to protect Palau’s environment. It’s probably the first passport stamp ever that has its own website.
Samoa


Nothing particular to tell about the rather modern passport stamps. The Samoan entry form, however, demanded to name all countries visited during the last 30 days – on a space of 6 cm. After a month of island hopping in the Pacific, that was a bit of a challenge.
Solomon Islands


Apparently, it is possible to enter the Salomon Islands semi-legally from Bougainville in Papua New Guinea. The trip on little boats sounded very tempting to me, but a bit risky too. So I took the boring approach, which is a plane from Brisbane to Honiara, the capital. My first visit to Melanesia was still quite a cultural shock and quite different from what I had expected in Oceania.
Tuvalu


Tuvalu has just a little airport with few flights per week. Hence, there is just one person in charge of immigration checks, handling entry and departure at the same time: Those passengers passing on her right get an entry stamp, those on her left a departure stamp. The entry stamp features no data and has to be filled in by hand by the immigration officer. The departure stamp looks more modern.
Vanuatu


Vanuatu is rather strict on limiting your entry visa to the time you effectively spend there: I had to show the officer my onward ticket, and got an entry stamp that allowed me to stay only until my day of departure.