Rashbam in Pesachim (102a) writes that if there is no compelling logic to rule stringently, then ruling leniently is not regarded as a more preferred option. Rather, it is the only option. The Rema in his responsa (§ 54) rules that one is not allowed to be stringent regarding an issue where there is no uncertainty.
Pischei Teshuvah (Yoreh Deah 116:10) cites a dispute amongst the Acharonim if one is permitted to be stringent for himself regarding a matter that has been permitted by the Torah, such as a prohibited matter that was nullified.
Bnei Yissachar writes that it is a mitzvah not to be stringent in such a situation.
The Tzlach writes that it is preferable to record the permitted ruling regarding a situation that may be subject to a Biblical prohibition, because if there would be uncertainty, we would be compelled to rule stringently. The Tanna would not be introducing a novel ruling if the ruling was that the matter is prohibited. Regarding a matter that may be subject to a Rabbinic prohibition, however, the reverse would be true. It is preferable to record the stringent ruling because if there would be uncertainty, we would rule leniently.