tramp provides commands for compilation of files on remote machines. In order to get them loaded, you need to require tramp-util.el:
(require 'tramp-util)
Afterwards, you can use the commands tramp-compile and
tramp-recompile instead of compile and recompile,
respectively; see Compilation. This does not
work for the ftp and smb methods.
The corresponding key bindings and menu entries calling these commands are redefined automatically for buffers associated with remote files.
After finishing the compilation, you can use the usual commands like
previous-error, next-error and first-error for
navigation in the *Compilation* buffer.