I'd capitalise 'President', just as I'd capitalise 'Queen', but I'm not 100% sure why. I think context may have something to do with it. I'm not sure I'd capitalise for less important queens and presidents and that worries me because it implies a lack of reciprocity.
I trust the current occupant will cure you of that problem. :-)
Don't shoot me! I'm only the messenger. :-)
I will quote relevant sections from CMOS below.
I suggested before some style guides have explicit exceptions for the Queen and the Pope.
Note that 8.22 states the exception for the Queen only applies in the "British Commonwealth".
I was wrong about the pope being an exception. The other exception is 'Speaker', mentioned in 8.21, which is an exception because the lowercase form of that word has a different, natural meaning.
8.18 Titles and offices - the general rule
Civil, military, religious, and professional titles are capitalized when they immediately precede a personal name and are thus used as part of the name (typically replacing the title holder's first name). In formal prose and other generic text (as opposed to promotional or ceremonial contexts or a heading), titles are normally lowercased when following a name or used in place of a name (but see 8.19). For abbreviated forms, see 10.11–27. President Lincoln; the president General Bradley; the general Cardinal Newman; the cardinal Governors Quinn and Paterson; the governors Although both first and second names may be used after a capitalized title (President Abraham Lincoln; but see 8.20)—and though it is perfectly correct to do so—Chicago prefers to avoid such usage in formal prose, especially with civil, corporate, and academic titles (see 8.21,8.26,8.27). Note also that once a title has been given, it need not be repeated each time a person's name is mentioned.
John F. Kerry, senator from Massachusetts; Senator Kerry; Kerry
8.19 Exceptions to the general rule
In promotional or ceremonial contexts such as a displayed list of donors in the front matter of a book or a list of corporate officers in an annual report, titles are usually capitalized even when following a personal name. Exceptions may also be called for in other contexts for reasons of courtesy or diplomacy.
Maria Martinez, Director of International Sales
A title used alone, in place of a personal name, is capitalized only in such contexts as a toast or a formal introduction, or when used in direct address.
Ladies and Gentlemen, the Prime Minister.
I would have done it, Captain, but the ship was sinking.
Thank you, Mr. President.
8.20 Titles used in apposition
When a title is used in apposition before a personal name—that is, not alone and as part of the name but as an equivalent to it, usually preceded by the or by a modifier—it is considered not a title but rather a descriptive phrase and is therefore lowercased.
the empress Elizabeth of Austria (but Empress Elizabeth of Austria)
German chancellor Angela Merkel (but Chancellor Merkel)
the German-born pope Benedict XVI
former president Carter
former presidents Reagan and Ford
the then secretary of state Colin Powell
8.21 Civil titles
Much of the usage below is contradicted by the official literature typically generated by political offices, where capitalization of a title in any position is the norm (see 8.19). In formal academic prose, however, civil titles are capitalized only when used as part of the name (except as noted). See also 10.13.
the president; George Washington, first president of the United States; President Washington; the presidency; presidential; the Washington administration; Washington; Gloria Macapagal Arroyo, president of the Philippines; President Arroyo; Arroyo
the vice president; John Adams, vice president of the United States; Vice President Adams; vice presidential duties
the secretary of state; Hillary Clinton, secretary of state; Secretary of State Clinton or Secretary Clinton
the senator; the senator from New York; New York senator Kirsten E. Gillibrand (see ); Senator Gillibrand; Senators Gillibrand and Schumer; Senator Mikulski, Democrat from Maryland (or D-MD)
the representative; the congressman; the congresswoman; Jesse Jackson Jr., representative from Illinois orcongressman from Illinois; Congressman Jackson or Rep. Jesse Jackson Jr. (D-IL); Kay Granger, representative from Texas; Congresswoman Granger; the congresswoman or the representative; Representatives Jackson and Granger
the Speaker; Nancy Pelosi, Speaker of the House of Representatives; Speaker Pelosi (Speaker is best capitalized in all contexts to avoid conflation with generic speakers)
the chief justice; John G. Roberts Jr., chief justice of the United States; Chief Justice Roberts (see also 8.63)
the associate justice; Ruth Bader Ginsburg, associate justice; Justice Ginsburg; Justices Ginsburg and Stevens
the chief judge; Timothy C. Evans, chief judge; Judge Evans
the ambassador; Robert Holmes Tuttle, ambassador to the Court of St. James's or ambassador to the United Kingdom; Ambassador Tuttle
the governor; Joe Manchin, governor of the state of West Virginia; Governor Manchin
the mayor; Richard M. Daley, mayor of Chicago; Mayor Daley
the state senator; Teresa Fedor, Ohio state senator; the Honorable Teresa Fedor
the state representative (same pattern as state senator)
the governor general of Canada; the Right Honourable Michaëlle Jean
the finance minister; Pranab Kumar Mukherjee, finance minister of India; Mukherjee
the prime minister; the Right Honourable Pierre Elliott Trudeau, former prime minister of Canada; Gordon Brown, the British prime minister
the premier (of a Canadian province); the Honourable Brad Wall
the member of Parliament (UK and Canada); Jane Doe, member of Parliament, or, more commonly, Jane Doe, MP; Jane Doe, the member for West Hamage
the chief whip; Nathi Mthethwa, chief whip of the African National Congress; Mthethwa
the foreign secretary (UK); the foreign minister (other nations); the British foreign secretary; the German foreign minister (not used as a title preceding the name)
the chancellor; Angela Merkel, chancellor of Germany; Chancellor Merkel
the chancellor of the exchequer (UK); Alistair Darling; Chancellor Darling
the Lord Privy Seal (UK; always capitalized)
For use of the Honorable and similar terms of respect, see 8.32,10.18.
8.22 Titles of sovereigns and other rulers
Most titles of sovereigns and other rulers are lowercased when used alone. See also 8.31.
King Abdullah II; the king of Jordan
Queen Elizabeth; Elizabeth II; the queen (in a British Commonwealth context, the Queen)
the Holy Roman emperor
Nero, emperor of Rome; the Roman emperor
Hamad ibn Isa al-Khalifah, king of Bahrain; King Hamad
the shah of Iran
the sharif of Mecca
the paramount chief of Basutoland
Wilhelm II, emperor of Germany; Kaiser Wilhelm II; the kaiser
the führer (Adolf Hitler)
Il Duce (used only of Benito Mussolini; both i and d capitalized)
8.23 Military titles
As is the case with civil titles, military titles are routinely capitalized in the literature of the organization or government with which they are associated. Nonetheless, in formal academic prose, most such titles are capitalized only when used as part of a person's name. Occasional exceptions may be made if ambiguity threatens. See also 10.13.
the general; General Ulysses S. Grant, commander in chief of the Union army; General Grant; the commander in chief
the general of the army; Omar N. Bradley, general of the army; General Bradley
the admiral; Chester W. Nimitz, fleet admiral; Admiral Nimitz, commander in chief of the Pacific Fleet
the chairman; Michael G. Mullen, chairman of the Joint Chiefs of Staff; Admiral Mullen
the captain; Captain Frances LeClaire, company commander
the sergeant; Sergeant Carleton C. Singer; a noncommissioned officer (NCO)
the warrant officer; Warrant Officer John Carmichael
the chief petty officer; Chief Petty Officer Tannenbaum
the private; Private T. C. Alhambra
the British general; General Sir Guy Carleton, British commander in New York City; General Carleton
For abbreviations, often used when a title precedes a name and appropriate in material in which many military titles appear, see 10.15.
8.25 Religious titles
Religious titles are treated much like civil and military titles (see 8.21, 8.23).
the rabbi; Rabbi Avraham Yitzhak ha-Kohen Kuk; the rabbinate
the cantor or hazzan; Deborah Bard, cantor; Cantor Bard
the sheikh; Sheikh Ibrahim el-Zak Zaky
the imam; Imam Shamil
the ayatollah; Ayatollah Khomeini
the Dalai Lama (traditionally capitalized); but previous dalai lamas
the sadhu; the guru; the shaman
the pope; Pope Benedict XVI; the papacy; papal
the cardinal; Francis Cardinal George or, less formally, Cardinal George; the sacred college of cardinals
the patriarch; Cyrillus Lucaris, patriarch of Constantinople; the patriarchate
the archbishop; the archbishop of Canterbury; Archbishop Williams (or, in this case, Dr. Williams)
the bishop; the bishop of Toledo; Bishop Donnelly; bishopric; diocese
the minister; the Reverend Shirley Stoops
the rector; the Reverend James Williams (see also 10.18.8.32)