The urn enhancer is an item that can be manufactured using the Invention skill. It requires level 24 Invention to discover. The blueprint used to discover how to make an urn enhancer is a reward from Nomad's Elegy. While the enhancer is in the inventory, each urn teleported grants 25% extra experience at a cost of 20 charges.
One divine charge will provide enough charges to enhance 150 urns, which gives an average cost of 672.42 coins per urn when charges are bought from the Grand Exchange.
When using the urn enhancer, one must consider the type of urns used. For expensive or high-experience urns, using the urn enhancer may be cheaper per point of experience than using the urns alone. For cheaper or lower-experience urns, it can be the other way around.
In terms of absolute efficiency, the enhancer is less efficient when used alongside urns which provide less experience as each urn consumes the same amount of charges regardless of how much experience it grants.
While exact values of experience vary between skills and might differ between players, a general figure of 10 coins per point of experience is a useful estimate. Using this figure, the urn enhancer would be worth using for all urns that provide more than 67.24 experience, even if it would be more expensive than using the urn alone.
Since almost all urns provide at least 67.24 experience, it can be concluded that the urn enhancer is worth using in almost all situations.