It is much easier if you use GNU Automake instead of writing your own Makefiles. If you do that you do not have to worry about finding and invoking the gpgme-config script at all. GPGME provides an extension to Automake that does all the work for you.
Check whether GPGME (at least version minimum-version, if given) exists on the host system. If it is found, execute action-if-found, otherwise do action-if-not-found, if given.
Additionally, the function defines
GPGME_CFLAGSto the flags needed for compilation of the program to find the gpgme.h header file, and
GPGME_LIBSto the linker flags needed to link the program to the GPGME library.
AM_PATH_GPGME_PTHchecks for the version of GPGME that can be used with GNU Pth, and defines
AM_PATH_GPGME_PTHREADchecks for the version of GPGME that can be used with the native pthread implementation, and defines
You can use the defined Autoconf variables like this in your Makefile.am:
AM_CPPFLAGS = $(GPGME_CFLAGS) LDADD = $(GPGME_LIBS)