With 3-cent and 7-cent stamps, the  ANSWER  is  11 cents.



    Indeed, it is easy to check that you can not 
    combine 11 cents using 3c and 7c stamps, only.


    From the other side, it is easy to prove that 
    you can combine any number of cents greater than 11, 
             using 3c and 7c stamps.



Indeed, 12 = 4*3;  13 = 7 + 2*3;  14 = 2*7.


Let N be the number of cents,  N >= 12.



    (a)  If N is a multiple of 3, you simply combine N as 
         the integer number    of 3c stamps.



    (b)  If N >= 12 gives the remainder 1 when divided by 3, then  (N-1)  
         is a multiple of 3, and you can combine N-1 cents using 3c stamps, only.

         In this combination, you will have at least four 3c stamps.


         Now from this combinations of 3c stamps, take off two 3c stamps and add 
         one 7c stamp - it will be your desired combination for N cents.



    (c)  If N >= 12 gives the remainder 2 when divided by 3, then  (N-2)  
         is a multiple of 3, and you can combine N-2 cents using 3c stamps, only.

         In this combination, you will have at least four 3c stamps.


         Now, from this combinations, take off four 3c stamps and add 
         two 7c stamps - it will be your desired combination for N cents.