Step 1: Oxidation numbers of chromium and manganese.
Chromium (Cr) can have an oxidation number of +6 in compounds like CrO\(_3\) (chromium trioxide). Manganese (Mn) can have an oxidation number of +7 in compounds like KMnO\(_4\) (potassium permanganate). Step 2: Conclusion.
Thus, the highest oxidation numbers are +6 for chromium and +7 for manganese, which corresponds to option (B).