Is it permissible to undergo medical examinations, such as semen analysis, for someone who has delayed conception?

There is no harm in taking measures and consulting doctors and undergoing examinations, as this does not contradict reliance on God. One of the greatest measures is supplicating to God, for God bestowed upon Zechariah, peace be upon him, John, while he was an old man and his wife was barren, after his supplication, as stated in Surat Maryam from verse 1 to 9. So, have a good opinion of God, for not conceiving for a period after marriage is common.