It is pronounced as /shil lye ham ni da /, with two l's, making a heavy /l/ sound.
If there was a word 실녜합니다, it would be pronounced like /실례함니다/, because ㄴ coming after a ㄹ usually becomes ㄹ.
For example, 실내(indoors) turns into /실래/, and 실낙원(Paradise Lost) /실락원/.
ㄹ-ㄴ sequence is nearly hard to pronounce accurately in Korean (but /례/ and /녜/ might not sound very distinctive after ㄹ).
You can also look up the dictionary (https://ko.dict.naver.com/detail.nhn?docid=23991700 for example).
If the word is pronounced specially, like 실례 becoming 실녜, it will list the actual pronunciation, but 실례 has no special listing, which means it's pronounced ordinarily. You could also listen to the pronunciation (the speaker icon).
hm.. I think 실례합니다 pronounced as shil lye ham ni da.
I'm not sure if it's helpful to you, but here link about it.
https://www.youtube.com/watch?v=SmkG-kJ4F2k
https://www.youtube.com/watch?v=u3ztW2oxyhU
(this is Shil lye song, just simple and cute)
Good luck! :D
when "ㄹ" is followed by another "ㄹ" , it is pronounced as /lr/
For example:
"실례합니다" is pronounced as pronounced as /shil rye ham ni da/