From the Guidelines

MRI with and without IV contrast is the indicated imaging modality for cervical and ovarian complex cysts.

MRI is the most useful modality for further evaluation of indeterminate lesions after sonographic evaluation, with an accuracy of >90% for the diagnosis of malignancy 1.
MRI can accurately identify solid tissue from nonsolid tissue and determine the origin of the lesion, with up to 9% of presumed adnexal lesions on US being nonadnexal origin 1.
The presence or absence of enhancing solid tissue and enhancement curve characteristics on perfusion dynamic contrast-enhanced imaging drives the risk of malignancy on MRI 1.
Contrast-enhanced MRI is particularly useful for sonographically visualized lesions >10 cm to ensure complete visualization and assessment of the lesion and ensure there are no associated solid components 1.
Evidence-based classification systems, such as the ADNEX MR system and the O-RADS MRI reporting system, have been proposed for standardized interpretation and characterization of adnexal lesions to improve risk-stratified management 1.
MRI with IV contrast is the modality of choice when an adnexal mass is indeterminate on US, with an overall accuracy of 91% for the diagnosis of malignancy 1.
The use of diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) values can also provide additional information, particularly in the setting of a low T2 signal mass 1.

From the Research

For cervical complex cysts, MRI can be used to differentiate between malignant and benign multicystic uterine cervical lesions, although it may not be possible to determine malignancy based on the existence of solid components, average cyst size, and signal intensity of cyst fluid 2.
For ovarian complex cysts, MRI provides better tissue characterization than Doppler ultrasound or CT-scan and is recommended in case of an indeterminate or complex ovarian ultrasonographic mass 3.
The protocol of a pelvic MRI for ovarian cysts should include morphological T1 and T2 sequences, and in case of solid portion, perfusion and diffusion sequences are recommended 3.
MRI is the technique of choice for differentiating between functional and organic ovarian lesion diagnosis 3.
The Ovarian-Adnexal Reporting and Data System (O-RADS) can be used to characterize complex adnexal cysts, with moderate interreader agreement for MRI and moderate concordance between US and MRI 4.

There is no specific mention of the use of contrast in the provided studies, but in general, contrast-enhanced MRI may be used to improve the visualization of lesions and to help differentiate between benign and malignant lesions.
However, the use of contrast should be determined on a case-by-case basis, taking into account the patient's medical history, kidney function, and other factors 3.

Pelvic MRI is preferred over CT-scan in case of doubt about the diagnosis of ovarian origin 3.
In pregnant patients, a risk-benefit balance should be evaluated case by case by the clinician and the radiologist, and information should be given to the patient 3.
MRI can be useful in case of clinical diagnostic uncertainty between polycystic ovary syndrome and ovarian hyperstimulation and multilocular ovarian tumor syndrome 3.