When a checked bag is delayed on an international flight, the Montreal Convention 1999 makes the airline liable for your reasonable replacement expenses (essentials you had to buy), up to about 1,519 SDR (~US$2,100 / €1,800) per passenger. There’s a hard 21-day deadline to complain in writing.

[Your name / address / email / phone]
[Date]
[Airline] — Baggage Claims

Re: Delayed baggage claim — Montreal Convention 1999, Article 19
    Flight [number] — [origin] to [destination] — [date]
    PIR / file reference: [____]   ·   Booking: [PNR]
    Bag tag number(s): [____]

Dear Sir or Madam,

My checked baggage on flight [number] on [date] was not delivered on
arrival. I reported it at [airport] and received Property Irregularity
Report reference [PIR]. The bag was [returned to me on [date], [X] days
late / still not returned as of this letter].

Under Article 19 of the Montreal Convention, the carrier is liable for
damage caused by delay in the carriage of baggage. I had to purchase
essential replacement items while without my belongings. I claim
reimbursement of the following reasonable expenses (receipts enclosed):

    [Item] ............................ [amount]
    [Item] ............................ [amount]
    ----------------------------------------------
    TOTAL ............................. [currency + amount]

This is within the per-passenger liability limit (currently 1,288 SDR
under the 2019 figures, raised to 1,519 SDR effective 28 December 2024).
Please reimburse [total] to [payment details] within 14 days.

Yours faithfully,
[Signature / printed name]

The 21-day clock is strict. Under Article 31, a written complaint for delayed baggage must reach the airline within 21 days of the bag being returned to you. Miss it and the claim is generally barred. (For damaged baggage it’s 7 days — see that letter.) You also have 2 years to file a lawsuit. File the airport PIR immediately and the written claim well inside 21 days.

Notes

Reasonable essentials only: toiletries, basic clothing, a phone charger — proportionate to the delay and your trip. Keep receipts. Some airlines pay a fixed daily interim amount; that doesn’t cap your reasonable actual costs up to the limit.
US domestic flight? The Montreal Convention doesn’t apply; the airline’s tariff governs, with DOT-set domestic liability up to $4,700 — see US passenger rights.
SDR fluctuates. 1 SDR ≈ US$1.37 and changes daily; see the Montreal Convention guide for current conversions.

Delayed baggage claim letter (Montreal Convention)