Dhikrullah protects against Satanic whispers:

Dhikrullah protects against Satan:

"He (God) enjoined upon you to remember God (do Dhikrullah). As the one who remembers his Lord is like a man who is chased by his enemy, but he reaches to a fortress where he saves himself from the enemy. Similarly a servant of God cannot save himself from the Satan but with the remembrance of God (Dhikrullah)". -Tirmidhi (Hasan-Sahih), Ahmed 

"If anyone withdraws himself from remembrance of (Allah) Most Gracious, We appoint for him a shaytan (devil), to be an intimate companion to him." (Quran- 43:36)

There is a famous Hadith mentioned by almost all the books of Hadiths in which Saeed Ibn Musayyib related from Samra Ibn Jundub (R.A) that one day the Messenger of God (S.A.W) related a long dream in which he saw a follower (ummati) being surrounded by Satans. Then the remembrance of God (he used to do) came and drove the Satans away.

-'al Wabil as sayyib' by Ibn AlQayyim R.A.

"Allah has built two houses in the heart of man, in one of which

an angel resides and in the other the Satan. The angel urges him to do good works and the Satan induces him to do evil works. When man remembers Allah, the Satan withdraws. And when he stops remembering Allah, the Satan perches on the heart of man and peeks with his beak to whisper into it to do evil things." [Transmitted by Abu Ya‘la on the authority of Anas رضي الله ﺗﻌﺎﻟﯽٰ عنه , as quoted by Tafsir    Mazhari- tafsir Mariful Quran].

Sayyiduna Anas ibn Malik (radiyallahu ‘anhu) reports that Rasulullah 
(sallallahu ‘alayhi wa sallam) said:
“Indeed Shaytan places his snout on the heart of Ibn Adam, when he 
remembers Allah he withdraws and when he becomes unmindful of Allah, 
then Shaytan devours/whispers into his heart, this is what is meant by 
‘Al Waswas’ and ‘Al Khannas’ [mentioned in Surah Nas].”
(Musnad Abu Ya’la, Hadith: 4301)

Although the above Hadith has been recorded with a weak chain, Hafiz Ibn 
Hajar (rahimahullah) has cited supporting weak narrations, which when combined, gain collective strength. The Hadith in question is suitable to quote.
(Refer: Fathul Bari, under Hadith: 4977)

Imam Bukhari (rahimahullah) has also recorded a similar narration as the 
statements of Sayyiduna ‘Abdullah ibn ‘Abbas (radiyallahu ‘anhuma) under the sub-heading and not part of the Sahih as this narration does not meet his strict criterion.
(Sahih Bukhari, before Hadith: 4977)

(Research on the last Hadith by: Moulana Suhail Motala on HadithAnswers.com)