The crate has to match a heavy, strong bird
A Muscovy travels in a large rigid dog crate with a solid floor, and sturdiness is the whole point. A mature drake is a big, muscular bird, far heavier than a mallard-type duck, and a flimsy carrier that flexes under his weight makes him brace and struggle. The crate should let him stand, turn and sit without his tail pressed to the door, with a floor that stays flat when he shifts. Wire floors are wrong for a Muscovy: his weight presses his feet through the grid, and his claws catch when he is lifted out at the other end.
Claws and wings: handling a Muscovy safely
A Muscovy defends itself with tools other ducks do not have. The claws on its feet are long and genuinely sharp, built for perching, and the wings are strong enough to batter. Catch the bird in a pen where it cannot build up flying speed, pin the wings gently against its body with one arm, and support the full weight from underneath with the other; never carry a Muscovy by its legs, because a heavy bird swinging from its leg joints can be badly hurt. Wear long sleeves, settle the bird into the crate facing away from the door, and close the door before you relax your hold.
A floor that grips and bedding that stays dry
A Muscovy rides best on a rubber mat or folded towel over the crate floor, with a layer of straw if the trip is long. The point is grip: a heavy bird sliding on smooth plastic slams real weight into the crate walls at every corner. Muscovies also produce wet droppings, and a long ride on soaked bedding leaves the bird chilled and filthy, so pack a spare towel for the trip home. Skip any water container inside the crate; a Muscovy will splash in it, bathe in it and empty it, in that order, within minutes.
In the car: level, covered and cool
A Muscovy settles fastest in a covered crate set level on the car floor where it cannot rock. Covering matters more for this breed than most: Muscovies are watchful birds that track movement, and a dim crate turns a vigilant drake placid. Keep the car cool, since a heavy, dark-feathered bird holds heat, and drive smoothly because every sharp brake throws serious weight forward. A Muscovy hen and drake that live together can travel in side-by-side crates within sight of each other if a shared crate would invite squabbling in a confined space.
At the clinic: warn them about the drake
A Muscovy should be flagged to the clinic before the crate door opens. Staff used to lighter ducks underestimate both the weight and the claws, and a Muscovy is examined most safely on a table with a towel over the wings and a second pair of hands. Keep the bird crated and covered in the waiting room, away from curious dogs, and lift it out only in the examination room with the door shut. Back home, open the crate inside the pen and let the bird step out to water under its own power. Bringing the Muscovy's weight history and past treatments in KinsLe's Pet Passport gives the vet a baseline for a bird whose size changes what normal looks like.