That's where you want to adapt Dave's solution:
some command | grep -eF 'Message is frozen'
will print only those lines of the output that don't contain the specified string: the 'F' flag means "treat the argument as a fixed string rather than as a regular expression", and the 'e' flag means "print lines that don't match" (normal behaviour being "print lines that do match").
If it really needs to match only lines where that string appears at the end of the line, you need a regular expression:
grep -e 'Message is frozen$'
.. in which the '$' matches end-of-line.
Be careful when extending this though: when the argument is a regular expression, various punctuation characters acquire special meanings, so you'll need to escape them (with a backslash) to match them literally.