com o grep você pode especificar o sinalizador -s que faz praticamente o que o @ortang disse
-s, --no-messages Suppress error messages about nonexistent or unreadable files. Portability note: unlike GNU grep, 7th Edition Unix grep did not conform to POSIX, because it lacked -q and its -s option behaved like GNU grep's -q option. USG-style grep also lacked -q but its -s option behaved like GNU grep. Portable shell scripts should avoid both -q and -s and should redirect standard and error output to /dev/null instead.
com o find, até onde eu sei, a resposta do @ortangs é a melhor. algo como
find / -name "myfile" -type f -print 2>/dev/null