Ancestral File and countless entries in Pedigree Resource File report Robert Morgan and Margaret Norman (see Norman-141) were married 27 January 1638; most seem to report Salem, Massachusetts, as the location. I find no such marriage in the published _Vital Records of Salem ..._ I have not otherwise found a historical record that includes any marriage date/location specifics.
Margaret Norman, bap. 1614, Charminster, Dorset, England, is placed in the colonies as early as 1626 To my knowledge, Robert Morgan’s migration hasn’t been placed.
The marriage date “27 January 1638” conflicts with modern, published reports that suggest record specifics for the union have yet to be discovered. Authors Walter Goodwin Davis, Robert Charles Anderson and Leslie Mahler report approximate dates for the marriage, always earlier than 1638. As the Norman baptismal records were located in 2002 and published by Mahler, that report may be the most informed--the marriage was placed at "about 1633."
As above, I have not located a historical record that speaks directly to the marriage date and location.
I do, however, find an unrelated record of “27:1: 1638” calling out Robert Morgan. See Salem Quarterly Court "27: 1: 1638" (ala, 27 March 1638). View the record as [Records and Files 1:7. Robert Morgan was fined for "being overseen in drink." http://hdl.handle.net/2027/mdp.35112104150240?urlappend=%3Bseq=20
Given the propensity to confuse old style dates, etc., it seems further likely records about two unrelated events were somehow conflated.
If folks are not able to improve on the understanding about the marriage information, might update we the marriage date to “about 1633,” thus inline with published account by Leslie Mahler (2002)?
Additional note and references follow. Pardon typos.--GeneJ
For an understanding that the 1638 court record date is at times reported as the marriage date, see a 2008 family genealogy  in which the author reports the marriage “Jan. 27, 1838,” without further reference. Citing the court record above, however, the author further comments
"first official notice of Robert found in Salem is a notation that he was fined for being "under the influence" on his wedding day in 1638."
 Citing "Bishops' Transcripts for Charminster, Dorsetshire, 1591-1879 [Family History Library, Salt Lake City, film #1,279,491, items 9-12]" in Leslie Mahler, "The English Origin of Richard Norman of Salem, Massachusetts," _The American Genealogist_ 77 (2002):102-103.
See separately, "England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/J3RK-QMQ : accessed 14 Apr 2014), Margret Norman, 04 Feb 1614; citing Charminster, Dorset, England, reference item 9; FHL microfilm 1279491.
 Walter Goodwin Davis, _The ancestry of Sarah Stone : wife of James Patten of Arundel (Kennebunkport) Maine_ (1930), p. 45-54, "Norman." Placed the Norman's in New England in 1626. http://hdl.handle.net/2027/wu.89066288291?urlappend=%3Bseq=61
 Robert Charles Anderson, _The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III_, 3 vols. (1995), 2:1334-1336 for "Richard Norman." Placed the Normans in New England, 1626; Morgan-Norman marriage as "by about 1633."
 Leslie Mahler, "The English Origin of Richard Norman of Salem, Massachusetts," _The American Genealogist_ 77 (2002):102-103. Reports about Margaret's baptism; places the marriage "by 1633"
 Gary Morgan, "The Ancestry of Stephen W. L. Morgan," December 2008 (unpaginated), pdf pages 4-5; digital images, FamilySearch (accessed via Family History Library Catalog, 2014)
Two published family histories that don't report the 1628 marriage date for Margaret and Robert:
(a) Edgar [Allan Poe] Yates. _The Yates Book: William Yates and His Descendants; the History and Genealogy of William Yates (1772-1868) of Greenwood, Maine, and His Wife, Who was Martha Morgan, together with the line of Her Descent from Robert Morgan of Beverly_ (1906); digital images, _Internet Archive_ (accessed 2013), p. 2 for Robert^1 Morgan in "The Line of Martha Morgan." http://archive.org/stream/yatesbookwilliam00yate#page/n11/mode/2up
(b) Betsey (Warren) Davis, _The Warren, Jackson and Allied Families: Being the Ancestry of Jesse Warren and Betsey Jackson_ (1903), 99-103 for "The Morgan and Norman Families"; digital images, _Internet Archive_ (accessed 2013), pp. 101-102 for Robert (1) Morgan. http://archive.org/stream/warrenjacksonall00davi#page/100/mode/2up
Update: Unseen work as Thomas and Jeanne Morgan, _Descendants of Robert Morgan of Essex County Massachusetts, 1601-2010_, Candy McMahan Perry, ed. (Rockland, Me.: Penobscot Press, 2010) in "Genealogies Recently Published," AmericanAncestors magazine 11.4 (2010)