This paper provides the result of a techno-economic study of potential energy storage technologies deployable at wind farms to provide short-term ancillary services such as inertia response and frequency support. Two different scenarios are considered including a single energy storage system for the whole wind farm and individual energy storage for each wind turbine (located at either the dc or the ac side of its grid-side converter). Simulations are introduced to check the technical viability of the proposal with different control strategies. Power and energy capability requirements demanded by both specific services are defined for each studied case based on present and future grid code needs. Based on these requirements, the study compares a wide range of energy storage technologies in terms of present-day technical readiness and properties and identifies potential candidate solutions. These are flywheels, supercapacitors, and three chemistries out of the Li-ion battery family. Finally, the results of a techno-economic assessment (mainly based on weight, volume, lifetime, and industry-confirmed costings) detail the advantages and disadvantages of the proposed solutions for the different scenarios under consideration. The main conclusion is that none of the candidates are found to be clearly superior to the others over the whole range of scenarios. Commercially available solutions have to be tailored to the different requirements depending on the amount of inertia, maximum Rate of Change of Frequency and maximum frequency deviation to be allowed.