Got it to work to read out the IMEI number.
// Initialize the GSM library instance
GSMClient client;
GPRS gprs;
GSM gsmAccess(true); // True for debugging
call gsmAccess.begin() so the modem is started... and then this function works:
String imei;
void readIMEI(){
GSM3ShieldV1DirectModemProvider modemAccess;
modemAccess.begin();
int tries = 10;
while (imei.length() < 15 && tries>0) {
imei = modemAccess.writeModemCommand("AT+GSN", 2000);
Serial.print(F("IMEI: "));
Serial.println(imei);
tries--;
}
int i;
String imei2="";
for (i=0;i<imei.length();i++) {
char a = imei[i];
Serial.println(a);
if (a >= '0' && a<='9') imei2 = imei2 + a; //Remove any characters except the numbers.
Serial.println(imei2);
}
imei = imei2;
}