awk '/$SearchString/{ print }' textfile.txt
This doesn't work, because the shell inhibits variable expansion between single quotes (').
awk /$SearchString'/{ print }' textfile.txt
What happens if $SearchString contains a space?
awk /"$SearchString"'/{ print }'
awk -v ss="$SearchString" '$0 ~ ss { print }'
The -v option is available with POSIX compliant awk implementations. mawk and gawk support it, but oawk does not. Some of the nawk impementations support it, some do not.