He answered with a smile upon his face, 'As I just told everybody else, you will have the results by the end of June.'

upon 是介词，表示"在...之上"，常用于书面语或正式场合，与 on 意思相近但更正式。在这里 upon his face 表示"在他脸上"，描述微笑所在的位置。