Both require quite some planning and logistics, which can be stressful and time-consuming for fur parents.
Rome's Fiumicino International Airport has sought to streamline the process by opening one of the first on-site hotels at a major European airport, following a similar initiative in Frankfurt.
Dog Relais' workers even retrieve pups from the terminal so travellers can proceed straight to their flight.
"This project is fitting into a strategy to provide a very immersive experience to passengers," said Marilena Blasi, chief commercial officer at Aeroporti di Roma, the company that manages the Italian capital's two airports.
"In this case, we provide services to dogs and the owners of the dogs."
Basic rooms at the dog hotel cost about $US47 ($A71) and feature temperature-controlled floors and private gardens.
More timid or solitary dogs can be placed in kennels at the edge of the facility, where they interact with staff rather than other dogs in the common grass pens.
At night, ambient music that has a frequency with a low, soft tone - 432 hertz - designed for relaxation is piped in through the rooms' speakers.
There are optional extras that range from the usual grooming, bathing and cleaning teeth services to the more indulgent, such as aromatherapy with lavender or peppermint scents to help induce calm, or arnica cream rubbed into aching muscles and joints.
Owners unsatisfied with standard-issue webcams for checking in on their canines from afar can spring for a $US70 ($A106) premium room equipped with a screen for round-the-clock video calls.
They can even pamper their pet by tossing a treat via an application connected to a dispenser.
The facility not only provides its services to travellers, but also to dog owners who need daycare.
Working in human resources for Aeroporti de Roma, Alessandra Morelli regularly leaves her two-year-old, chocolate-coloured Labrador Retriever there.
"Since I've been able to bring Nina to this dog hotel, my life, and the balance between my personal and professional life have changed because it allows me to enjoy my working day and my personal travels in total peace and tranquility," Morelli, 47, said.
Dario Chiassarini, 32, said he started bringing his Rottweiler puppy, Athena, to Dog Relais for training, another service on offer, because it's clean, well-organised and its location was easily accessible.
He said he planned to check his beloved pup into the hotel whenever he and his girlfriend needed to travel.
"We will rely on them without hesitation and without doubt - both because we got to know the people who work here, which for us is essential, and because of the love they have for animals and the peace of mind of knowing who we are entrusting Athena to," said Chiassarini, who works in car sales.
"It is certainly a service that, if we should need it, we will make use of."
The dog hotel has proved popular so far. All 40 rooms were occupied in August, when Italians take their customary summer holiday and millions of passengers come through Fiumicino.
Occupancy averaged almost two-thirds since doors opened in May, Blasi said.
The same month the dog hotel opened, Italy's commercial aviation authority changed rules to allow large dogs to fly inside plane cabins for domestic flights, provided they are inside secured crates.
The first such flight will take off on Tuesday, according to Transport Minister Matteo Salvini.
Salvini admits while many are happy with having their pups on the plane, others might feel annoyed.
"We always have to use judgment, but ... for me it's a source of pride, as well as a step forward from the point of view of civilisation," he told a pet conference on Tuesday.
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