Canada has no equivalent. The nearest structures — a charitable remainder trust under Canadian common law, or a gift of a residual interest — give a donation receipt for the present value of the residual interest, but they do not deliver the defining American feature, which is that the trust sells the appreciated asset without the donor realizing the gain and pays the donor an income stream back. In Canada, transferring appreciated property into a trust is generally a disposition at fair market value, so the gain lands first.

What does transfer is the narrower Canadian analogue: donating appreciated publicly traded securities in kind to a registered charity, where the capital gain inclusion rate on the donated shares is nil and the receipt is for full fair market value. That applies to marketable securities. It does not apply to your private company shares.