Siman 198

Three who ate and began to recite the blessing, and one who did not eat entered; if he entered when the one reciting the blessing said "Let us bless Him of whose bounty we have eaten" – he answers after them "Blessed and praised is His name always, forever and ever." Because when he hears the one reciting the blessing telling everyone to give a blessing to Hashem – all who hear are obligated to bless, for if not, it appears, Heaven forbid, as if he does not wish to… and because he is unable to say "of whose bounty we have eaten," since he did not eat – he shall say "Blessed and praised…".

But if he enters when those reclining answer "Blessed is He of Whose food we have eaten...", he answers "Amen" after them. And he does not need to say "Blessed," since he did not hear when he said "Let us bless." And it appears to me that the answering of "Amen" is after the leader repeats and says "Blessed is He of Whose food we have eaten...". For certainly every answering of "Amen" is at the end of the matter, and how could he not answer at the end? And if we were to say that he should answer after them and also after the leader, it is a wonderous thing to answer two "Amens" for one thing at almost the same moment. Therefore it appears to me as I have written. Furthermore, it appears to me that even one who enters at the time he says "Let us bless" and answers "Blessed and praised," nevertheless, he must answer "Amen" after "Blessed is He of Whose food we have eaten," for behold, for every blessing that he hears he is obligated to bless "Amen." And that which the Gemara and poskim distinguished between entering for "Let us bless" and entering for "Blessed," this is its explanation: that if he enters for "Let us bless" he must also say "Blessed," and if he enters for "Blessed" he shall only answer "Amen." And it is simple that if ten are blessing he should say "Blessed is our G-d and praised is His name always forever and ever." And if he drank water, and all the more so other drinks, and had not yet blessed the final blessing—he may answer "Blessed is He of Whose food we have eaten," for drinking is included in eating as I have written. And it is simple that there is no difference between one who enters at the time they began to bless, or if he sat there at the time of the meal and did not eat or drink. And so too if he comes at the time that the leader repeats and says "Blessed is He of Whose food we have eaten..."—he also answers "Amen." And there is one who disagrees on this, and it is not the primary view. (See Taz, and his words were not clarified. And also the Eliyah Rabbah took issue with him, see there. And the Gr"z ruled not to answer "Amen" when he answers "Blessed," and it requires further study. And also in siman 192, we ruled accordingly, see there.)