Making syscalls on Linux without a stack

Question

On Linux i386, the int $0x80 syscall ABI makes it easy to perform syscalls without having a valid userspace stack. The vdso/vsyscall interface, on the other hand, requires access to a stack. How do other Linux ports fare in this regard, especially x86_64? Do they have ways to make syscalls without a stack? Is there a reference on the available syscall methods for each arch?