Details of extant records on Archives Network Wales for the following;

• Miscellaneous papers in Caernarfon Probate Office 1709-1954
  "Caernarfon Probate Office was established in 1858, taking over responsibility for the proving of wills from the Diocese of Bangor..............."

Wills and Probate 1576-1858 : Caernarvonshire falls in the diocese of Bangor. Most wills from are available to view for free online at NLW Wills and are searchable using NLW Catalogue. Those that aren't available to view online (typically older records) can be viewed at the National Library of Wales / Llyfrgell Genedlaethol Cymru in Aberystwyth. 

Wills and Probate 1858- Present : Available to order on Gov.uk website. A year of death and surname are required.

Wills and Probate Records at the NLW.
Wills, which were proved in the Welsh ecclesiastical courts before the introduction of Civil Probate on 11 January 1858, have been deposited in the Library. The old indexes produced by the courts themselves have now been replaced by a new online index. Post-1858 wills for England and Wales are accessible at the Probate Dept of The Principal Registry Family Division:
Probate Search Room, First Avenue House, 42-49 High Holborn, London, WC1V 6NP.

Obituaries - (Of Welsh people of standing) - Cumulated Index: 1992 - 1997 - on the NLW site (Index is now online, scroll down left side menu)

• Post-1858 wills: copies can be ordered from the Probate Service or from UKDocuments for a  fee.
• Pre-1858 Wills: administrations and other probate records will be found in the Record Office holding the documents of the ecclesiastical (church) court where the will was proved.
• For English and Welsh records see TNA Leaflet: Will and Probate Records. Scottish testamentary records are held at the National Archives of Scotland in Edinburgh.
• Copies of wills proved in the Prerogative Court of Canterbury can be obtained for a fee from the National Archives via their Wills 1384-1858 page.
• Official search facility for finding the will of a soldier who died while serving in the British armed forces between 1850 and 1986.
• Tom's Wills - the index to UK wills 1931-1949.