A quick look hasn't yielded much; I came across a Stacey Grimaldi (1790-1863), a lawyer and antiquary, who apparently came into the title on the death of his brother in 1835. Both were sons of William Grimaldi (1751-1830) of Albemarle Street, London, a miniature painter, who according to the 1885-1900 DNB (on Wikisource) was son of Alexander Grimaldi, and great-grandson of Alessandro Maria Grimaldi (1659-1732), 'heir and representative of the noble Genoese family of Grimaldi, who settled in England after the bombardment of Genoa in 1684'. Another source I found (Collecting Miniatures by Daphne Foskett, 1979) states he was the '6th Marquess'.
Apparently Stacey Grimaldi had six sons and three daughters; these are of course possible candidates for ancestor of Philip Ranier Beaufort Grimaldi, 15th Marquis, but I'll need to look into this in more detail tomorrow I think to see if anything comes together (unless anyone gets there first!).
EDIT: This user-generated site shows amongst the children of Stacey Grimaldi several bearing the name 'Beaufort' which looks promising.
I've found Philip R. B. Grimaldi (1912-1983; m. 1940, Phyllis Anne Twigg), son of - Grimaldi and - Dyke, but can't find a record for his parents' marriage, which would be helpful... these current Grimaldis definitely appear to be of Stacey Grimaldi's line, given the 'Beaufort', though. I'll see what I can find tomorrow.
EDIT AGAIN: Actually, scotch that- Armorial Families has the Grimaldis as follows:
Rev. Ernest Craven dei Marchesi Grimaldi 1876- of Budleigh Salterton, Devons. m. 1911, Evelyn Lander, dau. of C. W. P. Dyke, of Totteridge
- Philip Rainier (sic?) Beaufort Grimaldi 1912-
- Christopher Beaufort Grimaldi 1916-
- Antony Beaufort Grimaldi 1918-
- Martin Cyril Beaufort Grimaldi 1920-
Ernest Grimaldi (the third son, implying his elder brothers' issue, if any, is extinct) was son of 'Rev. Marquess' Henry Beaufort Grimaldi 1831-1907 m. 1864, Sarah Sophia, dau. of William Rogers
The source gives 'Ernest George Grimaldi, 12th Marquess Grimaldi 1885- m. 1907, Mabel Joss, dau. of John Gray, of Aberdeen' as father of the 13th Marquess, George Frederick Ernest Grimaldi; the connection between the 13th Marquess and the above 'Rev. Marquess' Henry Beaufort Grimaldi isn't clarified.
I've found that Henry Beaufort Grimaldi 1831-1907 is one of the abovementioned Stacey Grimaldi's sons; which of his elder brothers (presumably) held and transmitted the Marquisate the same source neglects to provide. No mention is made of 'Ernest George Grimaldi', apparently the 12th Marquess, so all I can conclude is that at some point it passed to Henry Beaufort Grimaldi's line.
George Frederick Grimaldi (allegedly claimant of the title of 11th Marquis/ Marquess) was apparently a butcher, of Smithfield Market in London, based on a 1924 article in the Aberdeen Press and Journal announcing his death. A 1930 article mentions 'Ernest', claiming to be '12th Marquess', which fits the Armorial Families outline above. The London Gazette of 1956, vol. 4, pg 5942, states that George Frederick Ernest Grimaldi is a publican, of The Chequers, Ightham, Sevenoaks, Kent.
According to Ruvigny's 'Nobilities of Europe'. however, the 11th Marquis was Stacey William Beaufort Grimaldi, of Durban, Natal, S.A., with his heir his brother Henry Wynford Grimaldi; these are both sons of the Rev. Henry Beaufort Grimaldi, as above, as was Ernest Craven Grimaldi. I'm... not really sure (not at this time of day!) where they/ Ruvigny got things wrong...