What models are those Cisco switches?

If you can stack them, then yes - You can connect them in stack and aggregate ports from both of them to the servers, and connections will work.

If you can't stack them, but you can connect them together, you can still connect the servers to both of them, but you won't be able (propably) aggregate ports from both of them, as this requires features like VSS and/or mLACP. Still - rather higher-end gear.

At the worst possible case, you connect server to two different switches and pray Spanning Tree will work correctly, closing one of the connections for forwarding the traffic. Otherwise, you may end up with loop in the network, or periodic loop, and they're hard to troubleshoot or nail down in non-trivial topologies given limited instrumentation on the host with two NICs.

What models are those Cisco switches?

If you can stack them, then yes - You can connect them in stack and aggregate ports from both of them to the servers, and connections will work.

If you can't stack them, but you can connect them together, you can still connect the servers to both of them, but you won't be able (propably) aggregate ports from both of them, as this requires features like VSS and/or mLACP. Still - rather higher-end gear.

At the worst possible case, you connect server to two different switches and pray Spanning Tree will work correctly, closing one of the connections for forwarding the traffic. Otherwise, you may end up with loop in the network, or periodic loop, and they're hard to troubleshoot or nail down in non-trivial topologies given limited instrumentation on the host with two NICs (this assumes NIC driver can actually participate in the SPT, some of them can't and you'll end up with two separate links to both switches - which will work also, but isn't what you've asked for).