[13] Giving the album a rating of 8.0 out of 10, Pitchfork compared the album to the works of art rock legends David Bowie and Kate Bush and complimented its unique brand of sonic experimentation, nothing that the album "takes the more challenging route of twisting already twisted structures and unusual instrumentation to make them sound perfectly natural and, most importantly, easy to listen to as she overdubs her thrillingly sui generis vision into vibrant life".

[12] Marisa Brown of AllMusic, praising the album's inclusion of disparate elements, called it "one of the better indie pop albums that's come around for a long time"[14] Comparing Annie Clark's "knack for grandiose orchestrations" to that of former bandmate Sufjan Stevens, Vladimir Wormwood of PopMatters notes that she "tempers these more restlessly than Sufjan.

"[15] In a retrospective assessment of the record for its 10th anniversary, Margaret Farrell of Stereogum commended its ability to question love and marriage as a social institution.

She concluded that "Marry Me made it obvious that [Clark] would have a prosperous career exposing listeners to new points of view and cunning soundscapes".

[16] Similarly, Joe Marvilli of Spectrum Culture considers that Marry Me foreshadows the acclaim of Clark's subsequent releases, asserting that "her debut may not have the same impact or cohesiveness of latter albums, but it’s a wonderful example of an artist just starting out and carrying themselves with a confidence that will take them far.