Somebody has experience in the Integration of JIRA and SERVICE NOW with Webmethods
as long as there is an API (like REST, JSON, WebService etc.) exposed by those tools it should be able to integrate with webMethods.
Additionally, check SAG Integration Cloud if you have in-built connectors to connect JIRA and ServiceNow.
Basically you can use CloudStreams server and install connectors for Jira and ServiceNow to implement the logic for your application if you’re running on webMethods On-Premise.
On the other hand, Integration Cloud also provides recipes for you to use if you intend to connect to Jira or ServiceNow.
If you’re looking for more information on details of how to map an object in Jira to an object in ServiceNow, you can purchase ebook in packtpub.com for these two endpoints. There are plenty of information there where you could get some ideas.