The very best of Christian leave-taking allows room for the grief and sadness even while supported by faith in eternal life. The manner in which our funeral rites are celebrated seems to have struck a balance between the stark solemnity and judgement-fearing funerals of pre-Vatican II days and the celebratory, dutifully joyful funerals immediately following the Council. Now there is room for grief and mourning in a context of hope and faith. Tears and sadness are a true expression of the human condition and not necessarily a betrayal of our faith in eternal life; they are not out of place, they are perfectly in context.
As one of the Eucharist prayers for funerals affirms, "life is changed, not ended." Farewell, but not forever.