I picked from where Crypt32 left, used JNA to access the certificates using the same windows dialog that pops up if you were to use any windows specific program:
NativeLibrary cryptUI = NativeLibrary.getInstance("Cryptui");
NativeLibrary crypt32 = NativeLibrary.getInstance("Crypt32");
Function functionCertOpenSystemStore = crypt32.getFunction("CertOpenSystemStoreA");
Object[] argsCertOpenSystemStore = new Object[] { 0, "CA"};
HANDLE h = (HANDLE) functionCertOpenSystemStore.invoke(HANDLE.class, argsCertOpenSystemStore);
Function functionCryptUIDlgSelectCertificateFromStore = cryptUI.getFunction("CryptUIDlgSelectCertificateFromStore");
System.out.println(functionCryptUIDlgSelectCertificateFromStore.getName());
Object[] argsCryptUIDlgSelectCertificateFromStore = new Object[] { h, 0, 0, 0, 16, 0, 0};
Pointer ptrCertContext = (Pointer) functionCryptUIDlgSelectCertificateFromStore.invoke(Pointer.class, argsCryptUIDlgSelectCertificateFromStore);
Function functionCertGetNameString = crypt32.getFunction("CertGetNameStringW");
char[] ptrName = new char[128];
Object[] argsCertGetNameString = new Object[] { ptrCertContext, 5, 0, 0, ptrName, 128};
functionCertGetNameString.invoke(argsCertGetNameString);
System.out.println("Selected certificate is " + new String(ptrName));
Function functionCertFreeCertificateContext = crypt32.getFunction("CertFreeCertificateContext");
Object[] argsCertFreeCertificateContext = new Object[] { ptrCertContext};
functionCertFreeCertificateContext.invoke(argsCertFreeCertificateContext);
Function functionCertCloseStore = crypt32.getFunction("CertCloseStore");
Object[] argsCertCloseStore = new Object[] { h, 0};
functionCertCloseStore.invoke(argsCertCloseStore);
It is just a piece of code that works; feel free to apply your coding practices.