Max TCP Ports Per Container?

Newbie question. Normally, the max number of TCP client ports on a Linux server is 65535. On a busy server, that can be limiting. For example, a server running many instances of tomcat, where each instance makes many connections to various database servers, can fail to open a socket because all available client ports are already in use. Do containers work around that problem? Is there a separate client port limit for each container or pod?